Trigonometry Examples

Solve for x in Degrees 3cos(x)tan(x)=-5tan(x)
Step 1
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 1.1
Add parentheses.
Step 1.2
Reorder and .
Step 1.3
Rewrite in terms of sines and cosines.
Step 1.4
Cancel the common factors.
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Separate fractions.
Step 2.2.2
Rewrite in terms of sines and cosines.
Step 2.2.3
Multiply by the reciprocal of the fraction to divide by .
Step 2.2.4
Write as a fraction with denominator .
Step 2.2.5
Cancel the common factor of .
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Step 2.2.5.1
Cancel the common factor.
Step 2.2.5.2
Rewrite the expression.
Step 2.2.6
Move the negative in front of the fraction.
Step 2.2.7
Combine and .
Step 2.2.8
Move to the left of .
Step 2.3
Simplify the right side.
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Step 2.3.1
Cancel the common factor of .
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Step 2.3.1.1
Cancel the common factor.
Step 2.3.1.2
Rewrite the expression.
Step 2.3.2
Cancel the common factor of .
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Step 2.3.2.1
Cancel the common factor.
Step 2.3.2.2
Rewrite the expression.
Step 3
Multiply both sides of the equation by .
Step 4
Simplify both sides of the equation.
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Step 4.1
Simplify the left side.
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Step 4.1.1
Simplify .
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Step 4.1.1.1
Cancel the common factor of .
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Step 4.1.1.1.1
Move the leading negative in into the numerator.
Step 4.1.1.1.2
Move the leading negative in into the numerator.
Step 4.1.1.1.3
Factor out of .
Step 4.1.1.1.4
Cancel the common factor.
Step 4.1.1.1.5
Rewrite the expression.
Step 4.1.1.2
Cancel the common factor of .
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Step 4.1.1.2.1
Factor out of .
Step 4.1.1.2.2
Cancel the common factor.
Step 4.1.1.2.3
Rewrite the expression.
Step 4.1.1.3
Multiply.
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Step 4.1.1.3.1
Multiply by .
Step 4.1.1.3.2
Multiply by .
Step 4.2
Simplify the right side.
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Step 4.2.1
Multiply by .
Step 5
The range of cosine is . Since does not fall in this range, there is no solution.
No solution