Question

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

Options

•  1

• −1

• \[\sqrt{3}\]

• \[\frac{1}{\sqrt{3}}\]

Answer 1

Given that:  sin θ=cos (20-45°) and θ and 2θ-45 are acute angle 

We have to find  tan θ 

⇒` sin θ=cos (2θ-45°)` 

⇒`90°-θ=2θ-45θ` 

⇒`3θ=135°` 

Where θ and` 2θ-45°`  are acute angles

Since `θ =45°` 

Now

tan θ 

 = tan 45°   Put θ=45° 

=1