Question

(sin A + cosec A)°2 + (cos A + sec A) ^2 = 7 + tan2 A + cot2 A​

Answer 1

LHS = (sinA+cosecA)² + (cosA + secA)²

= sin²A+cosec²A+2sinAcosecA +cos²A+sec²A+2cosAsecA

= sin²A+cos²A+cosec²A+sec²A+2sinAcosecA+2cosAsecA

= 1 + cosec²A + sec²A + 2 + 2

$We \:know \:that ,$

• sin²A + cos²A = 1
• sinAcosecA = 1
• cosAsecA = 1

= 5 + ( 1+ cot²A ) + ( 1 + tan² A )

By Trigonometric identities:

• cosec²A = 1 + cot²A
• sec²A = 1 + tan²A

= 7 + tan²A + cot²A

= RHS

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