Question

Sin(3π/2-a)+cos(π+a)

Answer 1

-cos a -cos a = -2cos a 

Answer 2

Sin(3π/2-a)+cos(π+a)=-cosa-cosa=-2cosa

Answer 3

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You asked me to answer in detail: Sin(3π/2-a)+cos(π+a)

Using the trigonometric identities, we can simplify this expression as follows:

$$ \begin{aligned} \sin(3\pi/2-a)+\cos(\pi+a) &= -\cos(a)+\cos(\pi)\cos(a)-\sin(\pi)\sin(a) \\ &= -\cos(a)-\cos(a) \\ &= -2\cos(a) \end{aligned} $$

Therefore, the final answer is $$-2\cos(a)$$

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