Trigonometry Examples

Solve for ? 1/(1-sin(x))+1/(1+sin(x))=2sec(x)^2
Step 1
Simplify the left side.
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Step 1.1
Simplify .
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Step 1.1.1
To write as a fraction with a common denominator, multiply by .
Step 1.1.2
To write as a fraction with a common denominator, multiply by .
Step 1.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 1.1.3.1
Multiply by .
Step 1.1.3.2
Multiply by .
Step 1.1.3.3
Reorder the factors of .
Step 1.1.4
Combine the numerators over the common denominator.
Step 1.1.5
Simplify the numerator.
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Step 1.1.5.1
Add and .
Step 1.1.5.2
Subtract from .
Step 1.1.5.3
Add and .
Step 2
Multiply both sides by .
Step 3
Simplify.
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Step 3.1
Simplify the left side.
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Step 3.1.1
Cancel the common factor of .
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Step 3.1.1.1
Cancel the common factor.
Step 3.1.1.2
Rewrite the expression.
Step 3.2
Simplify the right side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Rewrite in terms of sines and cosines.
Step 3.2.1.2
Combine fractions.
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Step 3.2.1.2.1
Apply the product rule to .
Step 3.2.1.2.2
One to any power is one.
Step 3.2.1.2.3
Combine and .
Step 3.2.1.3
Expand using the FOIL Method.
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Step 3.2.1.3.1
Apply the distributive property.
Step 3.2.1.3.2
Apply the distributive property.
Step 3.2.1.3.3
Apply the distributive property.
Step 3.2.1.4
Simplify and combine like terms.
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Step 3.2.1.4.1
Simplify each term.
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Step 3.2.1.4.1.1
Multiply by .
Step 3.2.1.4.1.2
Multiply by .
Step 3.2.1.4.1.3
Multiply by .
Step 3.2.1.4.1.4
Rewrite using the commutative property of multiplication.
Step 3.2.1.4.1.5
Multiply .
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Step 3.2.1.4.1.5.1
Raise to the power of .
Step 3.2.1.4.1.5.2
Raise to the power of .
Step 3.2.1.4.1.5.3
Use the power rule to combine exponents.
Step 3.2.1.4.1.5.4
Add and .
Step 3.2.1.4.2
Add and .
Step 3.2.1.4.3
Add and .
Step 3.2.1.5
Apply pythagorean identity.
Step 3.2.1.6
Cancel the common factor of .
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Step 3.2.1.6.1
Cancel the common factor.
Step 3.2.1.6.2
Rewrite the expression.
Step 4
Since , the equation will always be true for any value of .
All real numbers
Step 5
The result can be shown in multiple forms.
All real numbers
Interval Notation: