Question

If sinθ = cosθ, then find the value of 2tanθ + cos^2 θ.

Answer 1

$\sin( \alpha ) = \cos( \alpha ) \\ \\ \alpha = \frac{\pi}{4} \\ \\ y = \: 2 \tan( \alpha ) + { \cos }^{2} \alpha \\ \\ y = 2 \tan( \frac{\pi}{4} ) + { \cos }^{2} (\frac{\pi}{4} ) \\ \\ y = 2(1) + ({ \frac{1}{ \sqrt{2} } )}^{2} \\ \\ \: \color{purple}\boxed{ y = 2 + \frac{1}{2} = \bf \frac{5}{2} }$

Answer 2

Answer:

Step-by-step explanation:

★ TRIGONOMETRIC REDUCTIONS ★

Given that :

Sin θ = Cos θ

Possible for only one set

θ = π / 4

Now , required value : 2Tanθ + Cos²θ

2 Tan45° + Cos²45°

2 ( 1 ) + 1/2

5/2

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