Question

if sin A=cos A, find the value of 2tan² + sin² A-1​

Answer 1

Remember, sin^2a+cos^2a = 1,

Substitute that for 1.

2tan^2A + sin^2A-sin^2A-cos^2A.

This is equal to 2tan^2A-cos^2A

We know that tan^2 = sin^2/cos^2

(2sin^2a/cos^2a) - cos^2a

Now, we can make this 2(sinA/cosA)^2 - cos^2A.

Now, remember, sinA=cosA, so let’s substitute

2(cosA/cosA)^2 - cos^2A.

Then, the answer is 2 - cos^2A.

Now, if sin^2A + cos^2A = 1, and sinA = cosA,

Then, cos^2A + cos^2A = 1.

cos^2A = 1/2.

Substitute this into the equation above (4 lines above).

2–cos^2A = 2 - 1/2 = 1.5

The answer is 1.5.

Answer 2

Answer:

Remember, sin^2a+cos^2a = 1,

Substitute that for 1.

2tan^2A + sin^2A-sin^2A-cos^2A.

This is equal to 2tan^2A-cos^2A

We know that tan^2 = sin^2/cos^2

(2sin^2a/cos^2a) - cos^2a

Now, we can make this 2(sinA/cosA)^2 - cos^2A.

Now, remember, sinA=cosA, so let’s substitute

2(cosA/cosA)^2 - cos^2A.

Then, the answer is 2 - cos^2A.

Now, if sin^2A + cos^2A = 1, and sinA = cosA,

Then, cos^2A + cos^2A = 1.

cos^2A = 1/2.

Substitute this into the equation above (4 lines above).

2–cos^2A = 2 - 1/2 = 1.5

The answer is 1.5.