Question

proove that

(cos - sin)²+(cos + sin)² = 2​

Answer 1

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Answer 2

Correct Question:

Prove that (cosA - sinA)² + (cosA + sinA)² = 2

SOLUTION:

(cosA - sinA)² + (cosA + sinA)² = 2

We know that,

(a - b)² = a² + b² - 2ab

(a + b)² = a² + b² + 2ab

= cos²A + sin²A - 2cosA. sinA + cos²A + sin²A + 2cosA. sinA

= cos²A + sin²A + cos²A + sin²A

= 2(cos²A + sin²A)

We know that,

cos²A + sin²A = 1

= 2 (1)

= 2,,

LHS = RHS

Hence, proved!