Trigonometry Examples

Verify sec(x)-tan(x)sin(x)=1/(sec(x))
Step 1
Simplify .
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Step 1.1
Simplify terms.
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Step 1.1.1
Simplify each term.
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Step 1.1.1.1
Rewrite in terms of sines and cosines.
Step 1.1.1.2
Rewrite in terms of sines and cosines.
Step 1.1.1.3
Multiply .
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Step 1.1.1.3.1
Combine and .
Step 1.1.1.3.2
Raise to the power of .
Step 1.1.1.3.3
Raise to the power of .
Step 1.1.1.3.4
Use the power rule to combine exponents.
Step 1.1.1.3.5
Add and .
Step 1.1.2
Combine the numerators over the common denominator.
Step 1.2
Apply pythagorean identity.
Step 1.3
Cancel the common factor of and .
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Step 1.3.1
Factor out of .
Step 1.3.2
Cancel the common factors.
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Step 1.3.2.1
Multiply by .
Step 1.3.2.2
Cancel the common factor.
Step 1.3.2.3
Rewrite the expression.
Step 1.3.2.4
Divide by .
Step 2
Simplify .
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Step 2.1
Rewrite in terms of sines and cosines.
Step 2.2
Multiply by the reciprocal of the fraction to divide by .
Step 2.3
Multiply by .
Step 3
For the two functions to be equal, the arguments of each must be equal.
Step 4
Move all terms containing to the left side of the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Subtract from .
Step 5
Since , the equation will always be true.
Always true