If θ is an actute angle and sin θ = cos θ , then the value of 2 tan² θ +sin² θ -1 is equal to

If θ is an actute angle and sin θ = cos θ , then the value…

If $\theta$ is an actute angle and sin $\theta$ = cos $\theta$ , then the value of 2 tan² $\theta$ +sin² $\theta$ -1 is equal to

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Correct answer: D

Explanation

The correct answer is option 4 i.e. $\frac{3}{2}$

Given that sinθ=cosθ

⟹ sinθ/cosθ=1

⟹ tanθ=1

⟹ θ=45^o

∴ 2tan²θ+sin²θ−1=2tan²45+sin²45−1

=2(1)²+(1/ $\sqrt2$ )²−1

= $\frac{3}{2}$