Question

If 2 sin²A- cos²A = 2, then find the value of A.​

Answer 1

Step-by-step explanation:

If 2 sin^2 A - cos^2 A = 2, what is the value of A?

2 sin^2 A - cos^2 A = 2

2 sin^2 A - cos^2 A = 2(sin^2 A + cos^2 A)

2 sin^2 A - cos^2 A = 2sin^2 A + 2cos^2 A

3cos^2 A = 0

cos A = 0, or A = 90 deg or 180 deg.

Check: 2 sin^2 A - cos^2 A

= 2*sin^2 90 - cos^2 90

= 2*1–0= 2. Correct.

Hence A = 90 deg or 180 deg.

Answer 2

Answer:

2 sin2 A - cos2 A = 2

2 sin2 A - cos2 A = 2(sin2 A + cos2 A)

2 sin2 A - cos2 A = 2sin2 A + 2cos2 A

3cos2 A = 0 cos A = 0

A = 90 degree or 180 degree