Question

If sin$\theta$=cos$\theta$ , then find the value of 2tan$\theta$ + $cos^{2} \theta$

Answer 1

GIVEN–

$\sinθ \: = \cosθ$
NOW,

WE HAVE TO FIND THE VALUE OF

$2 \tanθ + { \cos}^{2} θ \\ 2 \frac{ \ \sinθ }{ \cosθ } + { \cos }^{2} θ$
putting cosθ in the place of sinθ { Given, sinθ=cosθ }

$2 \frac{ \cosθ}{ \cosθ } + { \cos}^{2} θ \\ 2 \times 1 + { \cos }^{2}θ \\ 2 + { \cos }^{2}θ$
so, the value of 2tanθ + cos²θ is 2+cos²θ

or

2+sin²θ

Answer 2

Answer:

Step-by-step explanation:

Given that,

Sinθ = cosθ

Cos(90° - θ) = Cosθ

By comparing the angles,

90 - θ = θ

θ = 90/2

θ = 45°

>>2tanθ + (cosθ)^2

= 2tan45° + (cos 45°)^2

= 2×1 + 1/2

= 2 + 1/2

= 5/2

Hope it helps you....

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