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)$\frac{1}{\sqrt{3} }$

Answer 1

SOLUTION :  

The correct option is (a) : 1

Given : sin θ = cos (2θ - 45°) and  θ and (2θ - 45°) are acute angles.

sin θ = cos (2θ - 45°)

cos (90° - θ) = cos (2θ - 45°)

[cos (90° - θ) = sin θ]

On equating both sides,

(90° - θ) =  (2θ - 45°)

90° + 45° =  2θ +  θ  

135° = 3θ

θ = 135°/ 3  = 45°  

θ = 45°  

The value of tan θ :

tan θ  = tan 45° = 1

[θ = 45°, tan 45° = 1]

Hence, the degree measure of tan θ is 1 .

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Answer 2

The correct option is a. 1