Question

Please help?! I need step by step instruction when evaluating sin(Cos^-1(4/5)+Tan^1(3/4)). What is an identity used in the solution?
a. cos2x = 1 - 2cos^2x
b. cos2x = sin^2x - cos^2x
c. sin2x = 1 - 2sin^2x
d. sin2x = 2sin x cos x

Answer 1

Do you know why one can say that

\[
\alpha = \tan^{-1} (3/4)= \cos^{-1}(4/5)
\]

Answer 2

You have to compute
\[
\sin(2 \alpha)
\]

Answer 3

\[
\sin(2\alpha) =2 \sin(\alpha) \cos(\alpha)= 2 \frac 3 5 \frac 4 5=\frac {24}{25}
\]
So the answer is d.

Answer 4

Oh o.k. I get it now. Thank you for the explanation and help!

Answer 5

yw