Question

if sin theta + cos theta equals to p and sin theta minus cos theta equals to Q then​

Answer 1

Answer:idk

Step-by-step explanation:

Answer 2

sin theta + cos theta equals to p and sin theta minus cos theta equals to Q then​

Given,

sin theta + cos theta = p

squaring on both sides, we get,

(sin theta + cos theta)² = (p)²

sin² theta + cos² theta + 2sin theta × cos theta = p² .........(1)

sin theta - cos theta = q

squaring on both sides, we get,

(sin theta - cos theta)² = (q)²

sin² theta + cos² theta - 2sin theta × cos theta = q² ............(2)

adding equations (1) and (2), we get,

sin² theta + cos² theta + 2sin theta × cos theta  + sin² theta + cos² theta - 2sin theta × cos theta = p² + q²

2 (sin² theta + cos² theta) = p² + q²

as we know that, sin² theta + cos² theta = 1

2 (1) = p² + q²

∴ p² + q² = 1