Find the value of tan(1/2sin^-1 15/17)

Question

and

sin[pi/2-cos(1/2)]

Thanks.

Answer 1

arcsin 15/17 suggests a 8-15-17 right triangle. The angle is 61.93 degrees. half of that is 30.96 degrees. The tangent of that is 0.600

There is a formula that says that tan (x/2) = sin x/(1 + cos x)
You can use that to write
tan [(1/2)sin^-1(15/17)] = (15/17)/[1 + 8/17)] = 15/25 = 3/5
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In the second problem, did you mean to write cos(1/2) or cos^-1(1/2) ? In the former case, use the formula for
cos(x - y)