Trigonometry Examples

Solve for t (sin(t)+cos(t))^2=1+sin(2t)
Step 1
Simplify the left side.
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Step 1.1
Simplify .
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Step 1.1.1
Rewrite.
Step 1.1.2
Rewrite as .
Step 1.1.3
Expand using the FOIL Method.
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Step 1.1.3.1
Apply the distributive property.
Step 1.1.3.2
Apply the distributive property.
Step 1.1.3.3
Apply the distributive property.
Step 1.1.4
Simplify and combine like terms.
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Step 1.1.4.1
Simplify each term.
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Step 1.1.4.1.1
Multiply .
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Step 1.1.4.1.1.1
Raise to the power of .
Step 1.1.4.1.1.2
Raise to the power of .
Step 1.1.4.1.1.3
Use the power rule to combine exponents.
Step 1.1.4.1.1.4
Add and .
Step 1.1.4.1.2
Multiply .
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Step 1.1.4.1.2.1
Raise to the power of .
Step 1.1.4.1.2.2
Raise to the power of .
Step 1.1.4.1.2.3
Use the power rule to combine exponents.
Step 1.1.4.1.2.4
Add and .
Step 1.1.4.2
Reorder the factors of .
Step 1.1.4.3
Add and .
Step 1.1.5
Move .
Step 1.1.6
Apply pythagorean identity.
Step 1.1.7
Simplify each term.
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Step 1.1.7.1
Reorder and .
Step 1.1.7.2
Reorder and .
Step 1.1.7.3
Apply the sine double-angle identity.
Step 2
Move all terms containing to the left side of the equation.
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Combine the opposite terms in .
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Step 2.2.1
Subtract from .
Step 2.2.2
Add and .
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: