QUESTION 3 (3.1) Let z = x+iy € C. Show that sin(z) = sin x cosh y + i cos x sinh y. (3.2) Write (-√√3+i) ³/2 in the form a + bi.

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A: We have to give an example of a value of z such that the equation sinx=z is unsolvable.

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A: Given,       (sec x + tan x) cos x - 1= sin x

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A: Explanation of the answer is as follows

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Q: 2. Simplify: cos(+ x) cos(-x) = sin(n + x) sin(x + 37)

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A: As per guideline we have to solve one question Please repost other question again

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A: As we know that Sinx-y=SinxCosy-CosxSinyThe genaral solution of Sinz=-1  then z=Sin-1-1=nπ±π2

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A: We have to prove that cosπ2+x=−sinx. Use formula cosA+B=cosAcosB−sinAsinB Here, A=π2 and B=x Hence,…

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A: Solution

Q: Prove that there is a real number r so that sin(r) = x – 1.

A: We have, sinx=x-1 Let us consider a function fx such that, fx=x-1-sinx