Question

given sec(theta)=5 find cos(90-theta)

Answer 1

first, sec(θ) = 1/sin(θ)
so,
sec(θ) = 5
1/cos(θ) = 5
cos(θ) = 1/5

then find sin(θ) by using this identity :
sin^2 (θ) + cos^2 (θ) = 1
so,
sin^2 (θ) + (1/5)^2 = 1
sin^2 (θ) = 1 - 1/25
sin^2 (θ) = 24/25
sin(θ) = sqrt(24/25) =1/5 sqrt(24) = 1/5 * 2sqrt(6) = 2/5 sqrt(6)

then use the identity of
cos(90-θ) = sin(θ)
therefore,
cos(90-θ) = sin(θ) = 2/5 sqrt(6)