Prove the identities sinx + cosx = 1 – 3 sinx cosx

Asked by Aaryan | 1 year ago |  70

##### Solution :-

Let us consider LHS: sinx + cosx

(sinx) 3 + (cosx) 3

By using the formula, a3 + b3 = (a + b) (a2 + b2 – ab)

(sinx + cosx) [(sinx) 2 + (cosx) 2 – sinx cosx]

By using the formula, sinx + cosx = 1 and a2 + b2 = (a + b) 2 – 2ab

1 × [(sinx + cosx) 2 – 2sinx cosx – sinx cosx

12 – 3sinx cosx

1 – 3sinx cosx

= RHS

∴ LHS = RHS

Hence proved.

Answered by Sakshi | 1 year ago

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