Trigonometry Examples

Solve for x (9+sin(x)^2)/(cos(x)^2)=10sec(x)^2-1
Step 1
Move all the expressions to the left side of the equation.
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Add to both sides of the equation.
Step 2
Simplify .
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Step 2.1
Simplify each term.
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Step 2.1.1
Rewrite in terms of sines and cosines.
Step 2.1.2
Apply the product rule to .
Step 2.1.3
One to any power is one.
Step 2.1.4
Combine and .
Step 2.1.5
Move the negative in front of the fraction.
Step 2.2
Combine the numerators over the common denominator.
Step 2.3
Subtract from .
Step 2.4
Rewrite as .
Step 2.5
Factor out of .
Step 2.6
Factor out of .
Step 2.7
Rewrite as .
Step 2.8
Apply pythagorean identity.
Step 2.9
Cancel the common factor of .
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Step 2.9.1
Cancel the common factor.
Step 2.9.2
Divide by .
Step 2.10
Subtract from .
Step 3
Since , the equation will always be true for any value of .
All real numbers
Step 4
The result can be shown in multiple forms.
All real numbers
Interval Notation: