QuestionApril 19, 2025

Express as a trigonometric function of one angle. cos2sin(-1)-cos1sin2 square

Express as a trigonometric function of one angle. cos2sin(-1)-cos1sin2 square
Express as a trigonometric function of one angle. cos2sin(-1)-cos1sin2 square

Solution
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Answer

-sin(1) Explanation 1. Use the angle subtraction formula The expression cos(2)sin(-1) - cos(1)sin(2) can be rewritten using the angle subtraction identity for sine: **sin(a - b) = sin(a)cos(b) - cos(a)sin(b)**. 2. Apply the formula Set a = 2 and b = 1. Then, sin(2 - 1) = sin(2)cos(1) - cos(2)sin(1). 3. Simplify the expression Since sin(-1) = -sin(1), rewrite cos(2)sin(-1) - cos(1)sin(2) as -(cos(2)sin(1) - cos(1)sin(2)). 4. Finalize the expression This simplifies to -sin(2 - 1) = -sin(1).

Explanation

1. Use the angle subtraction formula<br /> The expression $cos(2)sin(-1) - cos(1)sin(2)$ can be rewritten using the angle subtraction identity for sine: **$sin(a - b) = sin(a)cos(b) - cos(a)sin(b)$**.<br />2. Apply the formula<br /> Set $a = 2$ and $b = 1$. Then, $sin(2 - 1) = sin(2)cos(1) - cos(2)sin(1)$.<br />3. Simplify the expression<br /> Since $sin(-1) = -sin(1)$, rewrite $cos(2)sin(-1) - cos(1)sin(2)$ as $-(cos(2)sin(1) - cos(1)sin(2))$.<br />4. Finalize the expression<br /> This simplifies to $-sin(2 - 1) = -sin(1)$.
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