If θ and 2θ – 45° are acute angles such that sin θ = cos (2θ – 45°), then tan θ is equal to

Question

Philoid · Accepted Answer

Given,

θ and 2θ – 45° are acute angle,

sin θ = cos (2θ – 45)………….. (i)

[∵ cos (90 – θ) = sin θ]

Putting these value in equation (i),

Cos (90 – θ) = cos (2θ – 45°)

90 - θ = 2 θ – 45°

90 + 45 = 3 θ

3 θ = 135

θ = 135/3 = 45

tan θ = tan 45° = 1