Mathway | المسائل الشائعة

المسائل الشائعة

التصنيف	الموضوع	المسألة	مسألة منسّقة
15001	بسّط	( الجذر التربيعي لـ 6)/4+( الجذر التربيعي لـ 2)/4	$\frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}$
15002	بسّط	( الجذر التربيعي لـ 3)/4	$\frac{\sqrt{3}}{4}$
15003	بسّط	( الجذر التربيعي لـ 33)/( الجذر التربيعي لـ 55)	$\frac{\sqrt{33}}{\sqrt{55}}$
15004	بسّط	(1-cos(t)^2)/(tan(t)^2)	$\frac{1 - \cos^{2} (t)}{\tan^{2} (t)}$
15005	بسّط	(1-cos(t)^2)/(cos(t))	$\frac{1 - \cos^{2} (t)}{\cos (t)}$
15006	بسّط	(1-cos(-x)^2)/(1+tan(-x)^2)	$\frac{1 - \cos^{2} (- x)}{1 + \tan^{2} (- x)}$
15007	بسّط	(1-cos(x)^2)/(1+cos(x))	$\frac{1 - \cos^{2} (x)}{1 + \cos (x)}$
15008	بسّط	(1-sin(x)^2)/(1-sin(x))	$\frac{1 - \sin^{2} (x)}{1 - \sin (x)}$
15009	بسّط	(1-sin(a)^2)/(2cos(a))	$\frac{1 - \sin^{2} (a)}{2 \cos (a)}$
15010	بسّط	(1-sin(t)^2)/(cot(t)^2)	$\frac{1 - \sin^{2} (t)}{\cot^{2} (t)}$
15011	بسّط	(1-sin(x)^4)/(1+sin(x)^4)	$\frac{1 - \sin^{4} (x)}{1 + \sin^{4} (x)}$
15012	بسّط	\|ac+ci\|	$\| a c + c i \|$
15013	بسّط	(1-(cos(x)+sin(x))(cos(x)+sin(x)))/(sin(x)cos(x))	$\frac{1 - (\cos (x) + \sin (x)) (\cos (x) + \sin (x))}{\sin (x) \cos (x)}$
15014	بسّط	\|-3+2i\|	$\| - 3 + 2 i \|$
15015	بسّط	\|-4+3i\|	$\| - 4 + 3 i \|$
15016	بسّط	(z^2-36)/(z^2+36)	$\frac{z^{2} - 36}{z^{2} + 36}$
15017	بسّط	\|x+2\|+\|2x-1\|-\|x-1\|	$\| x + 2 \| + \| 2 x - 1 \| - \| x - 1 \|$
15018	بسّط	(y^2-16)/(y^2)*(y^2-4x)/(x^2+2x-24)	$\frac{y^{2} - 16}{y^{2}} \cdot \frac{y^{2} - 4 x}{x^{2} + 2 x - 24}$
15019	بسّط	(y^3-8)/(2y^3)*(4y)/(y^2-5y+6)	$\frac{y^{3} - 8}{2 y^{3}} \cdot \frac{4 y}{y^{2} - 5 y + 6}$
15020	بسّط	((x^2-25)/14)÷((x-5)/28)	$\frac{x^{2} - 25}{14} \div \frac{x - 5}{28}$
15021	بسّط	(x^2-23)/(2x^5-5x-3)+-1/(2x+1)	$\frac{x^{2} - 23}{2 x^{5} - 5 x - 3} + \frac{- 1}{2 x + 1}$
15022	بسّط	(x^2-5x+6)/(x^2-4x)*(x-4)/(x-3)	$\frac{x^{2} - 5 x + 6}{x^{2} - 4 x} \cdot \frac{x - 4}{x - 3}$
15023	بسّط	(x^2-6x+9)/(6x-18)	$\frac{x^{2} - 6 x + 9}{6 x - 18}$
15024	بسّط	(x^2-8x+15)/(x^2-4x-5)*(x^(2-1))/(x^2-9)	$\frac{x^{2} - 8 x + 15}{x^{2} - 4 x - 5} \cdot \frac{x^{2 - 1}}{x^{2} - 9}$
15025	بسّط	(tan(x)+cot(x))/(sec(x)^2)	$\frac{\tan (x) + \cot (x)}{\sec^{2} (x)}$
15026	بسّط	(sin(x)-cos(x))^2-1	${(\sin (x) - \cos (x))}^{2} - 1$
15027	بسّط	(tan(7x)+tan(5x))/(1-tan(7x)tan(5x))	$\frac{\tan (7 x) + \tan (5 x)}{1 - \tan (7 x) \tan (5 x)}$
15028	بسّط	(-x+1)^2	${(- x + 1)}^{2}$
15029	بسّط	(x+4)/(2x-4)*(8x^2-32)/(x^2-16)	$\frac{x + 4}{2 x - 4} \cdot \frac{8 x^{2} - 32}{x^{2} - 16}$
15030	بسّط	(sin(x)-cos(x))^2-(sin(x)+cos(x))^2	${(\sin (x) - \cos (x))}^{2} - {(\sin (x) + \cos (x))}^{2}$
15031	بسّط	(sin(x)csc(x))/(tan(x))	$\frac{\sin (x) \csc (x)}{\tan (x)}$
15032	بسّط	(sin(x)cos(x))^2	${(\sin (x) \cos (x))}^{2}$
15033	بسّط	(sin(2x)-tan(x))/(cos(2x))	$\frac{\sin (2 x) - \tan (x)}{\cos (2 x)}$
15034	بسّط	(sin(x)+cos(x))^4	${(\sin (x) + \cos (x))}^{4}$
15035	بسّط	(sin(t)-cos(t))^2	${(\sin (t) - \cos (t))}^{2}$
15036	بسّط	(-sin(x))^2	${(- \sin (x))}^{2}$
15037	بسّط	((sin(x)-cos(x))(sin(x)-cos(x))-1)/(sin(x)cos(x))	$\frac{(\sin (x) - \cos (x)) (\sin (x) - \cos (x)) - 1}{\sin (x) \cos (x)}$
15038	بسّط	(sin(30+x)-cos(60+x))/(sin(30+x)+cos(60+x))	$\frac{\sin (30 + x) - \cos (60 + x)}{\sin (30 + x) + \cos (60 + x)}$
15039	بسّط	(sec(x)-cos(x))^2-(sec(x)+cos(x))^2	${(\sec (x) - \cos (x))}^{2} - {(\sec (x) + \cos (x))}^{2}$
15040	بسّط	(csc(x)-sin(x))/(cot(x))	$\frac{\csc (x) - \sin (x)}{\cot (x)}$
15041	بسّط	(rcos(1)+5)^2	${(r \cos (1) + 5)}^{2}$
15042	بسّط	(cos(30)+isin(30))^18	${(\cos (30) + i \sin (30))}^{18}$
15043	بسّط	(rcos(x))^2	${(r \cos (x))}^{2}$
15044	بسّط	(cos(x)+1)^2	${(\cos (x) + 1)}^{2}$
15045	بسّط	(cot(x)+tan(x))^2-(cot(x)-tan(x))^2	${(\cot (x) + \tan (x))}^{2} - {(\cot (x) - \tan (x))}^{2}$
15046	بسّط	(cot(x)-1)/(1-tan(x))	$\frac{\cot (x) - 1}{1 - \tan (x)}$
15047	بسّط	(cot(x)-1)^2	${(\cot (x) - 1)}^{2}$
15048	بسّط	(csc(6x)+cot(6x))/(csc(6x)-cot(6x))	$\frac{\csc (6 x) + \cot (6 x)}{\csc (6 x) - \cot (6 x)}$
15049	بسّط	(cos(0)+cos(0))^2+(cos(0)+cos(0))^2	${(\cos (0) + \cos (0))}^{2} + {(\cos (0) + \cos (0))}^{2}$
15050	بسّط	(cos(x)-cos(x))^2+(cos(x)+cos(x))^2	${(\cos (x) - \cos (x))}^{2} + {(\cos (x) + \cos (x))}^{2}$
15051	بسّط	(cos(t)-1)/(sec(t)-1)	$\frac{\cos (t) - 1}{\sec (t) - 1}$
15052	بسّط	(cos(t)-sec(t))^2	${(\cos (t) - \sec (t))}^{2}$
15053	بسّط	(3(cos(48)+isin(48)))^5	${(3 (\cos (48) + i \sin (48)))}^{5}$
15054	بسّط	((cos(3x)+isin(3x))^5(cos(4x)+isin(4x))^4)/((cos(5x)+isin(5x))^3(cos(6x)+isin(6x))^2)	$\frac{{(\cos (3 x) + i \cdot \sin (3 x))}^{5} \cdot {(\cos (4 x) + i \cdot \sin (4 x))}^{4}}{{(\cos (5 x) + i \cdot \sin (5 x))}^{3} \cdot {(\cos (6 x) + i \cdot \sin (6 x))}^{2}}$
15055	بسّط	(sec(x)^2-9)/(3+sec(x))-sec(x)	$\frac{\sec^{2} (x) - 9}{3 + \sec (x)} - \sec (x)$
15056	بسّط	(tan(x)^3(x)-sec(x)^2xtan(x))/(cot(-x))	$\frac{\tan^{3} (x) (x) - \sec^{2} (x) x \tan (x)}{\cot (- x)}$
15057	بسّط	(cos(30)^2)^2(30)-sin(-60)	${(\cos^{2} (30))}^{2} (30) - \sin (- 60)$
15058	بسّط	(z-3)^3	${(z - 3)}^{3}$
15059	بسّط	(3(cos(100)+isin(100)))^3	${(3 (\cos (100) + i \sin (100)))}^{3}$
15060	بسّط	(x+y)^3-(x-y)^3	${(x + y)}^{3} - {(x - y)}^{3}$
15061	بسّط	(sin(x)^2)/(cos(x))+(cos(x))/1	$\frac{\sin^{2} (x)}{\cos (x)} + \frac{\cos (x)}{1}$
15062	بسّط	(sin(x)^2)/(sec(x)^2-1)	$\frac{\sin^{2} (x)}{\sec^{2} (x) - 1}$
15063	بسّط	(sin(x)^2-2sin(x)+1)/(sin(x)-1)	$\frac{\sin^{2} (x) - 2 \sin (x) + 1}{\sin (x) - 1}$
15064	بسّط	(sin(x)^2-9)/(2cos(x)+1)*(10cos(x)+5)/(3sin(x)+9)	$\frac{\sin^{2} (x) - 9}{2 \cos (x) + 1} \cdot \frac{10 \cos (x) + 5}{3 \sin (x) + 9}$
15065	بسّط	(sin(x)^2)/(cos(x)^2)-1/(cos(x)^2)	$\frac{\sin^{2} (x)}{\cos^{2} (x)} - \frac{1}{\cos^{2} (x)}$
15066	بسّط	(sin(x)^2-tan(x)^2)/(tan(x)^2sin(x)^2)	$\frac{\sin^{2} (x) - \tan^{2} (x)}{\tan^{2} (x) \sin^{2} (x)}$
15067	بسّط	(sin(x-9)^2)/(2cos(x+1))*(10cos(x+5))/(3sin(x+9))	$\frac{\sin^{2} (x - 9)}{2 \cos (x + 1)} \cdot \frac{10 \cos (x + 5)}{3 \sin (x + 9)}$
15068	بسّط	(sin(B)^2)/(cos(B))+cos(B)	$\frac{\sin^{2} (B)}{\cos (B)} + \cos (B)$
15069	بسّط	(sec(x)^4-tan(x)^4)/(sec(x)^2+tan(x)^2)	$\frac{\sec^{4} (x) - \tan^{4} (x)}{\sec^{2} (x) + \tan^{2} (x)}$
15070	بسّط	(sin(a)^8)/(sin(a)^2-cos(a)^2)-(cos(a)^8)/(sin(a)^2-cos(a)^2)	$\frac{\sin^{8} (a)}{\sin^{2} (a) - \cos^{2} (a)} - \frac{\cos^{8} (a)}{\sin^{2} (a) - \cos^{2} (a)}$
15071	بسّط	(sec(x)^2-1)/(csc(x)^2-1)	$\frac{\sec^{2} (x) - 1}{\csc^{2} (x) - 1}$
15072	بسّط	(sec(x)^2-1)/(tan(x))	$\frac{\sec^{2} (x) - 1}{\tan (x)}$
15073	بسّط	(sec(x)^2)/(csc(x)^2)	$\frac{\sec^{2} (x)}{\csc^{2} (x)}$
15074	بسّط	(sin(x)^2-4)/(2cos(x)+1)*(10cos(x)+5)/(2sin(x)+4)	$\frac{\sin^{2} (x) - 4}{2 \cos (x) + 1} \cdot \frac{10 \cos (x) + 5}{2 \sin (x) + 4}$
15075	بسّط	(sin(x)^2)/(csc(x)tan(x)^2)	$\frac{\sin^{2} (x)}{\csc (x) \tan^{2} (x)}$
15076	بسّط	(csc(t)^2-cot(t)^2)/(sin(t)^2)	$\frac{\csc^{2} (t) - \cot^{2} (t)}{\sin^{2} (t)}$
15077	بسّط	(cot(x)^2)/(1-sin(x)^2)+(tan(x)^2)/(1-cos(x)^2)	$\frac{\cot^{2} (x)}{1 - \sin^{2} (x)} + \frac{\tan^{2} (x)}{1 - \cos^{2} (x)}$
15078	بسّط	(cot(x)^2)/(csc(x))-csc(x)	$\frac{\cot^{2} (x)}{\csc (x)} - \csc (x)$
15079	بسّط	(d^2+d-30)/(d^2+3d-40)+(d^2+14d+48)/(d^2-2d-48)	$\frac{d^{2} + d - 30}{d^{2} + 3 d - 40} + \frac{d^{2} + 14 d + 48}{d^{2} - 2 d - 48}$
15080	بسّط	(pi/2)/(1/4)	$\frac{\frac{π}{2}}{\frac{1}{4}}$
15081	بسّط	(n^2)/(n-3)-9/(n-3)	$\frac{n^{2}}{n - 3} - \frac{9}{n - 3}$
15082	بسّط	(k^2+5k+6)/(k^2+11k+8)*(k^2+9k)/(k^2-2k-15)	$\frac{k^{2} + 5 k + 6}{k^{2} + 11 k + 8} \cdot \frac{k^{2} + 9 k}{k^{2} - 2 k - 15}$
15083	بسّط	(pi/4)/1	$\frac{\frac{π}{4}}{1}$
15084	بسّط	(pi/3)/(pi/2)	$\frac{\frac{π}{3}}{\frac{π}{2}}$
15085	بسّط	(pi/4+pi/2)/2	$\frac{\frac{π}{4} + \frac{π}{2}}{2}$
15086	بسّط	(pi/5)/2	$\frac{\frac{π}{5}}{2}$
15087	بسّط	sec(x)^2(3x)	$\sec^{2} (x) (3 x)$
15088	بسّط	(sec(theta)^2-tan(theta)^2)/(cot(theta)^2-csc(theta)^2)	$\frac{\sec^{2} (θ) - \tan^{2} (θ)}{\cot^{2} (θ) - \csc^{2} (θ)}$
15089	بسّط	(sec(t)^2-1)/(sec(t)^2)	$\frac{\sec^{2} (t) - 1}{\sec^{2} (t)}$
15090	بسّط	(sec(x)^2-cos(x)^2)/(tan(x)^2)	$\frac{\sec^{2} (x) - \cos^{2} (x)}{\tan^{2} (x)}$
15091	بسّط	(sec(x)^2-tan(x)^2)/(csc(x)^2)	$\frac{\sec^{2} (x) - \tan^{2} (x)}{\csc^{2} (x)}$
15092	بسّط	(pi/6)/4	$\frac{\frac{π}{6}}{4}$
15093	بسّط	(sec(x)^2)/(tan(x)+cot(x)^2tan(x))	$\frac{\sec^{2} (x)}{\tan (x) + \cot^{2} (x) \tan (x)}$
15094	بسّط	((3pi)/4)/2	$\frac{\frac{3 π}{4}}{2}$
15095	بسّط	((5pi)/6)/2	$\frac{\frac{5 π}{6}}{2}$
15096	بسّط	(27x^17y^18)/((x^5y^6)^(1/3))	$\frac{27 x^{17} y^{18}}{{(x^{5} y^{6})}^{\frac{1}{3}}}$
15097	بسّط	(1/(cos(x)))/(1/(cos(x)))	$\frac{\frac{1}{\cos (x)}}{\frac{1}{\cos (x)}}$
15098	بسّط	((2pi)/5)/4	$\frac{\frac{2 π}{5}}{4}$
15099	بسّط	(1/(sin(x)))/(sin(x))	$\frac{\frac{1}{\sin (x)}}{\sin (x)}$
15100	بسّط	(8/(y-7))/(9/(y-8))+(5/(y-8))/(4/(y-7))	$\frac{\frac{8}{y - 7}}{\frac{9}{y - 8}} + \frac{\frac{5}{y - 8}}{\frac{4}{y - 7}}$