Give the exact value of each expression without using a calculator.

Question

Give the exact value of each expression without using a calculator.

(a) 𝑐𝑜𝑠(2𝑐𝑜𝑠^ −1(2/5))

(b) 𝑠𝑖𝑛(𝑐𝑜𝑠^ −1(1/3)+𝑡𝑎𝑛^ −1(2))

Answer 1

a. We must use the trig identity cos(2x) = (-1 + 2cos²(x))

cos(2arccos(2/5))

= -1 + 2cos²(arccos(2/5))

= -1 + 2(2/5)²

= -17/25