Trigonometry Examples

Solve for x (cos(x))/(csc(x)-sin(x))=tan(x)
Step 1
Simplify the left side.
Tap for more steps...
Step 1.1
Rewrite in terms of sines and cosines.
Step 2
Simplify the right side.
Tap for more steps...
Step 2.1
Rewrite in terms of sines and cosines.
Step 3
Multiply both sides of the equation by .
Step 4
Multiply .
Tap for more steps...
Step 4.1
Combine and .
Step 4.2
Raise to the power of .
Step 4.3
Raise to the power of .
Step 4.4
Use the power rule to combine exponents.
Step 4.5
Add and .
Step 5
Cancel the common factor of .
Tap for more steps...
Step 5.1
Cancel the common factor.
Step 5.2
Rewrite the expression.
Step 6
Subtract from both sides of the equation.
Step 7
Simplify .
Tap for more steps...
Step 7.1
Convert from to .
Step 7.2
To write as a fraction with a common denominator, multiply by .
Step 7.3
Combine and .
Step 7.4
Combine the numerators over the common denominator.
Step 7.5
Simplify the numerator.
Tap for more steps...
Step 7.5.1
Apply the distributive property.
Step 7.5.2
Rewrite in terms of sines and cosines, then cancel the common factors.
Tap for more steps...
Step 7.5.2.1
Add parentheses.
Step 7.5.2.2
Reorder and .
Step 7.5.2.3
Rewrite in terms of sines and cosines.
Step 7.5.2.4
Cancel the common factors.
Step 7.5.3
Multiply .
Tap for more steps...
Step 7.5.3.1
Multiply by .
Step 7.5.3.2
Multiply by .
Step 7.5.3.3
Raise to the power of .
Step 7.5.3.4
Raise to the power of .
Step 7.5.3.5
Use the power rule to combine exponents.
Step 7.5.3.6
Add and .
Step 7.5.4
Multiply by .
Step 7.5.5
Rewrite as .
Step 7.5.6
Factor out of .
Step 7.5.7
Factor out of .
Step 7.5.8
Rewrite as .
Step 7.5.9
Apply pythagorean identity.
Step 7.5.10
Subtract from .
Step 7.6
Divide by .
Step 8
Since , the equation will always be true for any value of .
All real numbers
Step 9
The result can be shown in multiple forms.
All real numbers
Interval Notation: