Cos3A-sin3A/1-2sin2A= cosA + sinA. Prove the identity

Step-by-step explanation:

(cos(3A) − sin(3A)) / (1 − 2 sin(2A))

Use double angle formula:

(cos(3A) − sin(3A)) / (1 − 4 sin A cos A)

Use triple angle formulas:

(4 cos³A − 3 cos A − 3 sin A + 4 sin³A) / (1 − 4 sin A cos A)

Group and factor:

(4 (cos³A + sin³A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Factor the sum of cubes:

(4 (cos A + sin A) (cos²A − cos A sin A + sin²A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Use Pythagorean identity:

(4 (cos A + sin A) (1 − cos A sin A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Factor out cos A + sin A:

(cos A + sin A) (4 (1 − cos A sin A) − 3) / (1 − 4 sin A cos A)

Simplify:

(cos A + sin A) (4 − 4 cos A sin A − 3) / (1 − 4 sin A cos A)

(cos A + sin A) (1 − 4 cos A sin A) / (1 − 4 sin A cos A)

cos A + sin A

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4

is there any photos or whatever?