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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
\[\sqrt{3}\]
\[\frac{1}{\sqrt{3}}\]
Solution
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
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