Question

$(sin a + cos a)^{2} + (sin a - cos a) ^{2}$
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Answer 1

Given :-

• ( sin A + cos A )² + ( sinA - cosA)².

To Find :-

• Its simplified value.

Formulae Used :-

• ( a + b )² = a² + b² + 2ab .
• ( a - b )² = a² + b² - 2ab .
• sin² A + cos²A = 1 .

Solution :-

Given to us is : ( sin A + cos A )² + ( sinA - cosA)².

= ( sin A + cos A )² + ( sinA - cosA)².

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

= 1 + 1 + 2sinA.cosA - 2sinA.cosA

= 1 + 1 + 0.

= 2 .