Trigonometry Examples

Solve for x (sin(x)^2+2cos(x)-1)/(sin(x)^2+3cos(x)-3)=1/(1-sec(x))
Step 1
Subtract from both sides of the equation.
Step 2
Simplify .
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Step 2.1
Factor out of .
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Step 2.1.1
Factor out of .
Step 2.1.2
Factor out of .
Step 2.1.3
Factor out of .
Step 2.2
Move .
Step 2.3
Reorder and .
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
Multiply by .
Step 2.10
Simplify each term.
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Step 2.10.1
Factor out of .
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Step 2.10.1.1
Factor out of .
Step 2.10.1.2
Factor out of .
Step 2.10.1.3
Factor out of .
Step 2.10.2
Rewrite in terms of sines and cosines.
Step 2.11
To write as a fraction with a common denominator, multiply by .
Step 2.12
To write as a fraction with a common denominator, multiply by .
Step 2.13
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 2.13.1
Multiply by .
Step 2.13.2
Multiply by .
Step 2.13.3
Reorder the factors of .
Step 2.14
Combine the numerators over the common denominator.
Step 2.15
Simplify the numerator.
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Step 2.15.1
Apply the distributive property.
Step 2.15.2
Rewrite using the commutative property of multiplication.
Step 2.15.3
Move to the left of .
Step 2.15.4
Multiply .
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Step 2.15.4.1
Raise to the power of .
Step 2.15.4.2
Raise to the power of .
Step 2.15.4.3
Use the power rule to combine exponents.
Step 2.15.4.4
Add and .
Step 2.15.5
Expand using the FOIL Method.
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Step 2.15.5.1
Apply the distributive property.
Step 2.15.5.2
Apply the distributive property.
Step 2.15.5.3
Apply the distributive property.
Step 2.15.6
Simplify and combine like terms.
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Step 2.15.6.1
Simplify each term.
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Step 2.15.6.1.1
Multiply by .
Step 2.15.6.1.2
Cancel the common factor of .
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Step 2.15.6.1.2.1
Move the leading negative in into the numerator.
Step 2.15.6.1.2.2
Factor out of .
Step 2.15.6.1.2.3
Cancel the common factor.
Step 2.15.6.1.2.4
Rewrite the expression.
Step 2.15.6.1.3
Multiply by .
Step 2.15.6.1.4
Multiply by .
Step 2.15.6.1.5
Multiply by .
Step 2.15.6.1.6
Cancel the common factor of .
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Step 2.15.6.1.6.1
Move the leading negative in into the numerator.
Step 2.15.6.1.6.2
Factor out of .
Step 2.15.6.1.6.3
Cancel the common factor.
Step 2.15.6.1.6.4
Rewrite the expression.
Step 2.15.6.1.7
Multiply by .
Step 2.15.6.2
Add and .
Step 2.15.7
Apply the distributive property.
Step 2.15.8
Simplify.
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Step 2.15.8.1
Multiply by .
Step 2.15.8.2
Multiply by .
Step 2.15.9
Subtract from .
Step 2.15.10
Add and .
Step 2.15.11
Add and .
Step 2.15.12
Reorder and .
Step 2.15.13
Apply pythagorean identity.
Step 2.15.14
Subtract from .
Step 2.16
Divide by .
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: