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

and

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

Thanks.

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)

To find the value of tan(1/2sin^(-1)(15/17)), we can follow these steps:

Step 1: Use the inverse sine function to find the angle whose sine is (15/17).

sin^(-1)(15/17) ≈ 0.8901 radians.

Step 2: Divide the angle found in step 1 by 2.

(1/2) * 0.8901 ≈ 0.4451 radians.

Step 3: Use the tangent function to find the value of tan(0.4451).

tan(0.4451) ≈ 0.4923.

Therefore, the value of tan(1/2sin^(-1)(15/17)) is approximately 0.4923.

Now, let's move on to the second part:

To find the value of sin[π/2-cos(1/2)], we can follow these steps:

Step 1: Evaluate cos(1/2).

cos(1/2) ≈ 0.8776.

Step 2: Calculate π/2 - cos(1/2).

π/2 - cos(1/2) ≈ π/2 - 0.8776 ≈ 0.6947 radians.

Step 3: Use the sine function to find the value of sin(0.6947).

sin(0.6947) ≈ 0.6410.

Therefore, the value of sin[π/2-cos(1/2)] is approximately 0.6410.