Explain the concept

Explain the concept TRIGONOMETRIC FUNCTIONS Since P,P3 = P2P„ we have -P Therefore, 2 —2 (COS COS y — Sin x = 2 — 2 COS (x + y), Hence cos (x + y) = cos x cos y — sin sin y cos (x — y) = cos r cos y + sin x sin y Replacing y by —y m Identity 3, we get COS (x + y)) = COS x COS y) — sin x sin or COS (x — y) = COS x COS y + sin x sin y cos = sin x If we replace x by — and y by x in Identity we get —x) = cos — cosx + sin — cos sin x = sm x _ sin ( —— r) cos x Using the Identity 5, we have sin( —x) cos COS x. sin (r + y) —sin x cosy + cos x sin y We know that sin (x + y) sin (r — y) -(x+y) = cos —cos —x) COSY + sin —X) sin y = COS ( — — sin cos y + cos x sin y sm x cosy — cos x sm y If we replace by —y, in the Identity 7, we get the result. By Idking suitable values Of x and y in the identities 3, 4, 7 and 8, we get the following results: cos COS (It — x) — — COS x sin + r) sin (x — x) • cos x = Sin X