Trigonometry Examples

Solve for @VAR (2cos(t)-4sin(t))^2+(4cos(t)+2sin(t))^2=20
Step 1
Square 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 as .
Step 2.1.2
Expand using the FOIL Method.
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Step 2.1.2.1
Apply the distributive property.
Step 2.1.2.2
Apply the distributive property.
Step 2.1.2.3
Apply the distributive property.
Step 2.1.3
Simplify and combine like terms.
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Step 2.1.3.1
Simplify each term.
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Step 2.1.3.1.1
Multiply .
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Step 2.1.3.1.1.1
Multiply by .
Step 2.1.3.1.1.2
Raise to the power of .
Step 2.1.3.1.1.3
Raise to the power of .
Step 2.1.3.1.1.4
Use the power rule to combine exponents.
Step 2.1.3.1.1.5
Add and .
Step 2.1.3.1.2
Reorder and .
Step 2.1.3.1.3
Add parentheses.
Step 2.1.3.1.4
Reorder and .
Step 2.1.3.1.5
Apply the sine double-angle identity.
Step 2.1.3.1.6
Add parentheses.
Step 2.1.3.1.7
Reorder and .
Step 2.1.3.1.8
Apply the sine double-angle identity.
Step 2.1.3.1.9
Multiply .
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Step 2.1.3.1.9.1
Multiply by .
Step 2.1.3.1.9.2
Raise to the power of .
Step 2.1.3.1.9.3
Raise to the power of .
Step 2.1.3.1.9.4
Use the power rule to combine exponents.
Step 2.1.3.1.9.5
Add and .
Step 2.1.3.2
Subtract from .
Step 2.1.4
Rewrite as .
Step 2.1.5
Expand using the FOIL Method.
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Step 2.1.5.1
Apply the distributive property.
Step 2.1.5.2
Apply the distributive property.
Step 2.1.5.3
Apply the distributive property.
Step 2.1.6
Simplify and combine like terms.
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Step 2.1.6.1
Simplify each term.
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Step 2.1.6.1.1
Multiply .
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Step 2.1.6.1.1.1
Multiply by .
Step 2.1.6.1.1.2
Raise to the power of .
Step 2.1.6.1.1.3
Raise to the power of .
Step 2.1.6.1.1.4
Use the power rule to combine exponents.
Step 2.1.6.1.1.5
Add and .
Step 2.1.6.1.2
Add parentheses.
Step 2.1.6.1.3
Reorder and .
Step 2.1.6.1.4
Apply the sine double-angle identity.
Step 2.1.6.1.5
Reorder and .
Step 2.1.6.1.6
Add parentheses.
Step 2.1.6.1.7
Reorder and .
Step 2.1.6.1.8
Apply the sine double-angle identity.
Step 2.1.6.1.9
Multiply .
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Step 2.1.6.1.9.1
Multiply by .
Step 2.1.6.1.9.2
Raise to the power of .
Step 2.1.6.1.9.3
Raise to the power of .
Step 2.1.6.1.9.4
Use the power rule to combine exponents.
Step 2.1.6.1.9.5
Add and .
Step 2.1.6.2
Add and .
Step 2.2
Simplify terms.
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Step 2.2.1
Combine the opposite terms in .
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Step 2.2.1.1
Add and .
Step 2.2.1.2
Add and .
Step 2.2.2
Move .
Step 2.2.3
Factor out of .
Step 2.2.4
Factor out of .
Step 2.2.5
Factor out of .
Step 2.3
Rearrange terms.
Step 2.4
Apply pythagorean identity.
Step 2.5
Simplify with factoring out.
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Step 2.5.1
Factor out of .
Step 2.5.2
Factor out of .
Step 2.5.3
Factor out of .
Step 2.6
Apply pythagorean identity.
Step 2.7
Simplify terms.
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Step 2.7.1
Simplify each term.
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Step 2.7.1.1
Multiply by .
Step 2.7.1.2
Multiply by .
Step 2.7.2
Simplify the expression.
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Step 2.7.2.1
Add and .
Step 2.7.2.2
Raise to the power of .
Step 3
Raise to the power of .
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: