Question

cos⁻¹(sin π/7), Evaluate it.

Answer 1

answer : 5π/14

explanation : we have to find out value of cos⁻¹(sin π/7)

we know, sin(π/2 - θ) = cosθ

so, sin(π/7) = cos(π/2 - π/7) = cos(5π/14)

so,cos⁻¹(sin π/7) = cos⁻¹(cos(5π/14))

according to inverse trigonometric identities,

cos⁻¹(cosx) = x, when 0 ≤ x ≤ π

here x = 5π/14 in such a way that 0 ≤ (5π/14) ≤ π

so, cos⁻¹(cos(5π/14)) = 5π/14

hence, value of cos⁻¹(sin π/7) = 5π/14