Question

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

 A. 1 

B. - 1 

C. √3 

D. 1/√3

Answer 1

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 = 2θ – 45° 

90 + 45 = 3θ 

3θ = 135 

θ = 135/3 = 45 

tan θ = tan 45° = 1