Question

what is the value of 2tan²theta +cos²theta -2. if theta is an acute angle and sin theta = cos theta​

Answer 1

Answer:

1/2

Step-by-step explanation:

⇒ sinθ = cosθ

⇒ sinθ/cosθ = 1

⇒ tanθ = 1        ...(1)

Therefore,

⇒ tan²θ = 1

⇒ sec²θ - 1 = 1        {tan²θ = sec²θ - 1}

⇒ sec²θ = 2    ⇒ cos²θ = 1/2  ..(2)

Hence,

2tan²θ + cos²θ - 2

2(1) + (1/2) - 2

1/2

Answer 2

Answer:

Given :-

if theta is an acute angle and sin theta = cos theta

To Find :-

value of 2tan²theta +cos²theta

Solution :-

We are knowing that

sin theta = cos theta

sin theta/cos theta = 1

tan theta = 1 (1)

Now

tan² theta = 1²

tan²theta = 1

sec² theta - 1 = 1

sec² theta = 1 + 1

sec² theta = 2

Now,

cos² theta = sec²theta = ½

Now,

2(1)² + 1/2 - 2

2 × 1 + 1/2 - 2

2 + 1/2 - 2

(2 - 2) + 1/2

1/2