Question

If θ is measure of an acute angle and cosθ=sinθ, find the value of 2tan²θ+sin²θ+1.

Answer 1

Here, I am writing theta as A,

Now, Coming to the Question.

Given cosA = sinA

It can be written as

= > 1 = (sinA/cosA)

= > 1 = Tan A

= > Tan 45 = Tan A.

= > A = 45.

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Now,

= > 2 tan^2A + sin^2A + 1

= > 2tan^2(45) + sin^2(45) + 1

$= > 2(1) + (\frac{1}{\sqrt{2}})^2 + 1$

$= > 2 + \frac{1}{2} + 1$

$= > \frac{3 * 2 + 1}{2}$

$= > \frac{7}{2}$

Hope this helps!

Answer 2

HELLO DEAR,

your questions is--------------> If θ is measure of an acute angle and cosθ=sinθ, find the value of 2tan²θ+sin²θ+1.

GIVEN:- sinФ = cosФ

sinФ/cosФ = 1

⇒tanФ = tan45°

⇒Ф = 45°

so, 2tan²Ф + sin²Ф + 1

⇒2tan²45° + sin²45° + 1

⇒2(1)² + (1/√2)² + 1

⇒2 + 1/2 + 1

⇒3 + 1/2

⇒7/2


I HOPE ITS HELP YOU DEAR,
THANKS