verify the identity.\n\n\\( \\sin \\left( \\frac { 3 \\pi } { 2 } - \\theta \\right) = - \\cos \\theta…

verify the identity.\n\n\\( \\sin \\left( \\frac { 3 \\pi } { 2 } - \\theta \\right) = - \\cos \\theta \\)\n\nwrite the left side of the identity using a sum or difference formula for sine or cosine.\n\n\\( \\square \\) (do not simplify.)

verify the identity.\n\n\\( \\sin \\left( \\frac { 3 \\pi } { 2 } - \\theta \\right) = - \\cos \\theta \\)\n\nwrite the left side of the identity using a sum or difference formula for sine or cosine.\n\n\\( \\square \\) (do not simplify.)

Answer

Explanation:

Step1: Apply the sine difference formula

The formula for (\sin(A - B)=\sin A\cos B-\cos A\sin B). Here (A = \frac{3\pi}{2}) and (B=\theta). So we get (\sin\frac{3\pi}{2}\cos\theta-\cos\frac{3\pi}{2}\sin\theta)

Answer:

(\sin\frac{3\pi}{2}\cos\theta-\cos\frac{3\pi}{2}\sin\theta)