Solve for x:cos (arctan x) = √2/2 ?

Question

Also: 
Solve for θ: arcsin (1/secθ) = π/3 

Explanations for both questions are much appreciated! I will choose the answer with the best description. :) Thanks

 

 

Answer 1

• cos(tan^-1 x) = √2/2.

cos(tan^-1 x) = 1/√2

cos(tan^-1 x) = cos(π/4)

tan^-1 x = ± π/4

x = tan(- π/4) and x = tan(π/4)

x = - 1 and x = 1.

The solution is x = - 1 and x = 1.

• sin^{- 1} (1/sec θ) = π/3.

sin^{- 1} (cos θ) = π/3

cos θ = sin(π/3)

cos θ = √(3)/2

cos θ = cos (π/6).

The genaral solution of cos(θ) = cos(α) is θ = 2nπ ± α, where n is an integer.

θ = 2nπ ± (π/6).

The solution is θ = 2nπ ± (π/6).