Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
27401	Rationalize the Denominator	(1-cos(x))/(1+cos(x))*(sin(x))/(sin(x))	$\frac{1 - \cos (x)}{1 + \cos (x)} \cdot \frac{\sin (x)}{\sin (x)}$
27402	Rationalize the Denominator	(1-cos(2u))/(1+cos(2u))	$\frac{1 - \cos (2 u)}{1 + \cos (2 u)}$
27403	Rationalize the Denominator	2/(1-tan(x))	$\frac{2}{1 - \tan (x)}$
27404	Rationalize the Denominator	(2tan(x))/(1+tan(x)^2)	$\frac{2 \tan (x)}{1 + \tan^{2} (x)}$
27405	Rationalize the Denominator	(2tan(x/4))/(1-tan(x/4)^2)	$\frac{2 \tan (\frac{x}{4})}{1 - \tan^{2} (\frac{x}{4})}$
27406	Rationalize the Denominator	(2tan(3A))/(1-tan(3A)^2)	$\frac{2 \tan (3 A)}{1 - \tan^{2} (3 A)}$
27407	Rationalize the Denominator	(2tan(4x))/(1-tan(4x))	$\frac{2 \tan (4 x)}{1 - \tan (4 x)}$
27408	Rationalize the Denominator	(2tan(5x))/(1-tan(5x)^2)	$\frac{2 \tan (5 x)}{1 - \tan^{2} (5 x)}$
27409	Rationalize the Denominator	(2tan(7x))/(1-tan(7x)^2)	$\frac{2 \tan (7 x)}{1 - \tan^{2} (7 x)}$
27410	Rationalize the Denominator	(2tan(x)+7tan(y))/(1-tan(x)tan(y))	$\frac{2 \tan (x) + 7 \tan (y)}{1 - \tan (x) \tan (y)}$
27411	Rationalize the Denominator	(1-tan(x))/(1+tan(x))	$\frac{1 - \tan (x)}{1 + \tan (x)}$
27412	Rationalize the Denominator	(2(1/2)-2(1/4)-1)/(1-sin(45 degrees )^2)	$\frac{2 (\frac{1}{2}) - 2 (\frac{1}{4}) - 1}{1 - \sin^{2} (45 °)}$
27413	Rationalize the Denominator	(sec(t)tan(t))/(tan(t)^2+1)	$\frac{\sec (t) \tan (t)}{\tan^{2} (t) + 1}$
27414	Rationalize the Denominator	(2(tan(x/2)))/(1+tan(x)^2(x/2))=sin(x)	$\frac{2 (\tan (\frac{x}{2}))}{1 + \tan^{2} (x) (\frac{x}{2})} = \sin (x)$
27415	Find Where Undefined/Discontinuous	sin(3x)cos(x)=sin((5x)/2)cos((3x)/2)	$\sin (3 x) \cos (x) = \sin (\frac{5 x}{2}) \cos (\frac{3 x}{2})$
27416	Find Where Undefined/Discontinuous	(3/2)tan(x) = square root of 3/2	$(\frac{3}{2}) \tan (x) = \sqrt{\frac{3}{2}}$
27417	Find Where Undefined/Discontinuous	(1+sin(x))(1-sin(x))=cos(x)^2	$(1 + \sin (x)) (1 - \sin (x)) = \cos^{2} (x)$
27418	Find Where Undefined/Discontinuous	-(4m+2)-(-3m-5)=3	$- (4 m + 2) - (- 3 m - 5) = 3$
27419	Find Where Undefined/Discontinuous	x=arcsin(2)	$x = \arcsin (2)$
27420	Find Where Undefined/Discontinuous	x=-(11pi)/3	$x = - \frac{11 π}{3}$
27421	Rationalize the Denominator	(tan(x))/(1-cos(x)^2)	$\frac{\tan (x)}{1 - \cos^{2} (x)}$
27422	Rationalize the Denominator	(tan(pi/2-x)sec(x))/(1-csc(x)^2)	$\frac{\tan (\frac{π}{2} - x) \sec (x)}{1 - \csc^{2} (x)}$
27423	Rationalize the Denominator	(tan(pi/4)-tan(x))/(1+tan(pi/4)tan(x))	$\frac{\tan (\frac{π}{4}) - \tan (x)}{1 + \tan (\frac{π}{4}) \tan (x)}$
27424	Rationalize the Denominator	(tan(pi/8-x)+tan(pi/8+x))/(1-tan(pi/8-x)tan(pi/8+x))	$\frac{\tan (\frac{π}{8} - x) + \tan (\frac{π}{8} + x)}{1 - \tan (\frac{π}{8} - x) \tan (\frac{π}{8} + x)}$
27425	Rationalize the Denominator	(tan(27)+tan(28))/(1-tan(27)tan(28))	$\frac{\tan (27) + \tan (28)}{1 - \tan (27) \tan (28)}$
27426	Rationalize the Denominator	(tan(2y)+tan(3x))/(1-tan(2y)tan(3x))	$\frac{\tan (2 y) + \tan (3 x)}{1 - \tan (2 y) \tan (3 x)}$
27427	Rationalize the Denominator	(tan(4x)+tan(2x))/(1-tan(4x)tan(2x))	$\frac{\tan (4 x) + \tan (2 x)}{1 - \tan (4 x) \tan (2 x)}$
27428	Rationalize the Denominator	(tan(5x)-tan(4x))/(1+tan(5x)tan(4x))	$\frac{\tan (5 x) - \tan (4 x)}{1 + \tan (5 x) \tan (4 x)}$
27429	Rationalize the Denominator	(tan(83)+tan(37))/(1-tan(83)tan(37))	$\frac{\tan (83) + \tan (37)}{1 - \tan (83) \tan (37)}$
27430	Rationalize the Denominator	(tan(u)-tan(v))/(1+tan(u)tan(v))	$\frac{\tan (u) - \tan (v)}{1 + \tan (u) \tan (v)}$
27431	Rationalize the Denominator	(sin(x)cos(x))/(1-(sin(x)-cos(x))sin(x-cos(x)))	$\frac{\sin (x) \cos (x)}{1 - (\sin (x) - \cos (x)) \sin (x - \cos (x))}$
27432	Rationalize the Denominator	(sin(x/4))/(1+cos(x/4))	$\frac{\sin (\frac{x}{4})}{1 + \cos (\frac{x}{4})}$
27433	Rationalize the Denominator	(sin(2t))/(1+cos(2t))	$\frac{\sin (2 t)}{1 + \cos (2 t)}$
27434	Rationalize the Denominator	(sin(x))/(1-cos(x)^2)	$\frac{\sin (x)}{1 - \cos^{2} (x)}$
27435	Rationalize the Denominator	(sin(4x))/(1+cos(4x))	$\frac{\sin (4 x)}{1 + \cos (4 x)}$
27436	Rationalize the Denominator	(sin(-45))/(1+cos(-45))	$\frac{\sin (- 45)}{1 + \cos (- 45)}$
27437	Rationalize the Denominator	(sin(b))/(1+cos(b))	$\frac{\sin (b)}{1 + \cos (b)}$
27438	Subtract	2-19/4	$2 - \frac{19}{4}$
27439	Subtract	250-250/(tan(60))+500/(sin(60))	$250 - \frac{250}{\tan (60)} + \frac{500}{\sin (60)}$
27440	Subtract	2u-3u	$2 u - 3 u$
27441	Subtract	3sec(x)csc(x)-6csc(x)	$3 \sec (x) \csc (x) - 6 \csc (x)$
27442	Subtract	4(x^3+x^2-6)-3(2x^2-3x^2)	$4 (x^{3} + x^{2} - 6) - 3 (2 x^{2} - 3 x^{2})$
27443	Subtract	5cos(60)-4sin(60)	$5 \cos (60) - 4 \sin (60)$
27444	Subtract	6-5/(8y)	$6 - \frac{5}{8 y}$
27445	Subtract	arctan((xsin(y))/(1-xcos(y)))-arctan((x-cos(y))/(sin(y)))	$\arctan (\frac{x \sin (y)}{1 - x \cos (y)}) - \arctan (\frac{x - \cos (y)}{\sin (y)})$
27446	Subtract	cos((13pi)/5)cos(-pi/5)-sin((13pi)/5)sin(-pi/5)	$\cos (\frac{13 π}{5}) \cos (- \frac{π}{5}) - \sin (\frac{13 π}{5}) \sin (- \frac{π}{5})$
27447	Subtract	1/(cos(theta))-cos(theta)	$\frac{1}{\cos (θ)} - \cos (θ)$
27448	Subtract	pi/2-pi/7	$\frac{π}{2} - \frac{π}{7}$
27449	Subtract	cos(pi/4)cos(pi/12)-sin(pi/4)sin(pi/12)	$\cos (\frac{π}{4}) \cos (\frac{π}{12}) - \sin (\frac{π}{4}) \sin (\frac{π}{12})$
27450	Subtract	cos(pi/5)cos((2pi)/15)-sin(pi/5)sin((2pi)/15)	$\cos (\frac{π}{5}) \cos (\frac{2 π}{15}) - \sin (\frac{π}{5}) \sin (\frac{2 π}{15})$
27451	Subtract	cos(140)cos(20)-sin(140)sin(20)	$\cos (140) \cos (20) - \sin (140) \sin (20)$
27452	Subtract	cos(145)cos(85)-sin(145)sin(85)	$\cos (145) \cdot \cos (85) - \sin (145) \cdot \sin (85)$
27453	Subtract	cos(19)cos(11)-sin(19)sin(11)	$\cos (19) \cos (11) - \sin (19) \sin (11)$
27454	Subtract	cos(2x)-cos(4x)	$\cos (2 x) - \cos (4 x)$
27455	Subtract	cos(20)cos(70)-sin(20)sin(70)	$\cos (20) \cos (70) - \sin (20) \sin (70)$
27456	Subtract	cos(22)cos(66)-sin(22)sin(66)	$\cos (22) \cos (66) - \sin (22) \sin (66)$
27457	Subtract	cos(225)cos(300)-sin(225)sin(300)	$\cos (225) \cos (300) - \sin (225) \sin (300)$
27458	Subtract	cos(26)cos(34)-sin(26)sin(34)	$\cos (26) \cos (34) - \sin (26) \sin (34)$
27459	Subtract	cos(2pit)-1	$\cos (2 π t) - 1$
27460	Subtract	cos(2x)cos(3x)-sin(2x)sin(3x)	$\cos (2 x) \cos (3 x) - \sin (2 x) \sin (3 x)$
27461	Subtract	cos(35)cos(10)-sin(35)sin(10)	$\cos (35) \cos (10) - \sin (35) \sin (10)$
27462	Subtract	cos(35)cos(25)-sin(35)sin(25)	$\cos (35) \cos (25) - \sin (35) \sin (25)$
27463	Subtract	cos(39)cos(138)-sin(39)sin(138)	$\cos (39) \cos (138) - \sin (39) \sin (138)$
27464	Subtract	cos(3x)cos(x)-sin(3x)sin(x)	$\cos (3 x) \cos (x) - \sin (3 x) \sin (x)$
27465	Subtract	cos(40)cos(5)-sin(40)sin(5)	$\cos (40) \cos (5) - \sin (40) \sin (5)$
27466	Subtract	cos(45)cos(30)-sin(45)sin(30)	$\cos (45) \cos (30) - \sin (45) \sin (30)$
27467	Subtract	cos(x)-cos(2x)	$\cos (x) - \cos (2 x)$
27468	Subtract	cot(42)csc(48)-sin(42)	$\cot (42) \csc (48) - \sin (42)$
27469	Subtract	cot(x)-(csc(x)^2)/(cot(x))	$\cot (x) - \frac{\csc^{2} (x)}{\cot (x)}$
27470	Subtract	cot(x)-cot(x)	$\cot (x) - \cot (x)$
27471	Subtract	csc(x)-cos(x)cot(x)	$\csc (x) - \cos (x) \cot (x)$
27472	Subtract	csc(x)sec(x)-cot(x)	$\csc (x) \sec (x) - \cot (x)$
27473	Subtract	csc(-135)+sin(225)-tan(30)+tan(150)	$\csc (- 135) + \sin (225) - \tan (30) + \tan (150)$
27474	Subtract	csc(35)sec(55)-tan(55)cot(35)	$\csc (35) \sec (55) - \tan (55) \cot (35)$
27475	Subtract	pi-pi/4	$π - \frac{π}{4}$
27476	Subtract	sec(2x)-tan(2x)	$\sec (2 x) - \tan (2 x)$
27477	Add	sin(theta)+1/(cos(theta))	$\sin (θ) + \frac{1}{\cos (θ)}$
27478	Subtract	(28+3i)-(14-6i)	$(28 + 3 i) - (14 - 6 i)$
27479	Subtract	(6-i)-(9+4i)	$(6 - i) - (9 + 4 i)$
27480	Subtract	(cos(69))(cos(21))-sin(69)sin(21)	$(\cos (69)) (\cos (21)) - \sin (69) \sin (21)$
27481	Subtract	(sin(80)cos(70))-(cos(80)sin(70))	$(\sin (80) \cos (70)) - (\cos (80) \sin (70))$
27482	Subtract	1/(121/1)-1/((y^2)/1)	$\frac{1}{\frac{121}{1}} - \frac{1}{\frac{y^{2}}{1}}$
27483	Subtract	1/(1-sin(x))-1/(1+sin(x))	$\frac{1}{1 - \sin (x)} - \frac{1}{1 + \sin (x)}$
27484	Subtract	1/(sin(theta))-1/(cos(theta))	$\frac{1}{\sin (θ)} - \frac{1}{\cos (θ)}$
27485	Subtract	13/12-7/12	$\frac{13}{12} - \frac{7}{12}$
27486	Subtract	24/25-5/12	$\frac{24}{25} - \frac{5}{12}$
27487	Subtract	(2pi+4)/(6pi-6)-(3pi)/(6pi)	$\frac{2 π + 4}{6 π - 6} - \frac{3 π}{6 π}$
27488	Subtract	(2x)/(x^2-16)-1/(x-4)	$\frac{2 x}{x^{2} - 16} - \frac{1}{x - 4}$
27489	Subtract	5/(6a^2b)-4/(15ab^2)	$\frac{5}{6 a^{2} b} - \frac{4}{15 a b^{2}}$
27490	Subtract	(6x-11y)/(3x)-(9x-7y)/(3x)	$\frac{6 x - 11 y}{3 x} - \frac{9 x - 7 y}{3 x}$
27491	Subtract	7/(4p)-3/(2p^2)	$\frac{7}{4 p} - \frac{3}{2 p^{2}}$
27492	Subtract	8/d-3/5	$\frac{8}{d} - \frac{3}{5}$
27493	Subtract	(9x)/(2y-3x)-(5y)/(3x-2y)	$\frac{9 x}{2 y - 3 x} - \frac{5 y}{3 x - 2 y}$
27494	Subtract	pi/2-pi/90	$\frac{π}{2} - \frac{π}{90}$
27495	Subtract	(sec(x))/(csc(x)-cot(x))-(sec(x))/(csc(x)-cot(x))	$\frac{\sec (x)}{\csc (x) - \cot (x)} - \frac{\sec (x)}{\csc (x) - \cot (x)}$
27496	Subtract	(sec(x))/(sin(x))-(sec(x))/(csc(x))	$\frac{\sec (x)}{\sin (x)} - \frac{\sec (x)}{\csc (x)}$
27497	Subtract	arctan(34/x)-arctan(6/x)	$\arctan (\frac{34}{x}) - \arctan (\frac{6}{x})$
27498	Subtract	square root of 3-cos(15)^2- square root of 3sin(15)^2	$\sqrt{3} - \cos^{2} (15) - \sqrt{3} \sin^{2} (15)$
27499	Subtract	x/x-2/x	$\frac{x}{x} - \frac{2}{x}$
27500	Subtract	(x-1)/(x+2)-(4x-7)/(5x+10)	$\frac{x - 1}{x + 2} - \frac{4 x - 7}{5 x + 10}$