Find the exact value of the following Find the EXACT value o

Find the exact value of the following

Find the EXACT value of the following A: cos (2 tan^-1 (3/4)) sin(2sec^-1 (4)) cos (sin^-1(2/7)/2) sin (cot^-1(5)/2)

Solution

A. Cos (2tan^-1(3/4))

Tan^-1(3/4)=t

Tan t=3/4

Cos t=4/5

Cos 2t=2cos²t-1 =2(4/5)²-1= 7/25

Therefore cos(2 tan^-1(3/4))=7/25

B.sin(2sec^-1(4))

Sec^-14=t

Sec t=4

Cos t=1/4

Sin t=sqrt15/4

Sin 2t=2sin t cos t=sqrt15/8