(sin A + cosec A)°2 + (cos A + sec A) ^2 = 7 + tan2 A + cot2 A
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(sin A + cosec A)°2 + (cos A + sec A) ^2 = 7 + tan2 A + cot2 A
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LHS = (sinA+cosecA)² + (cosA + secA)²
= sin²A+cosec²A+2sinAcosecA +cos²A+sec²A+2cosAsecA
= sin²A+cos²A+cosec²A+sec²A+2sinAcosecA+2cosAsecA
= 1 + cosec²A + sec²A + 2 + 2
[tex] We \:know \:that ,[/tex]
= 5 + ( 1+ cot²A ) + ( 1 + tan² A )
By Trigonometric identities:
= 7 + tan²A + cot²A
= RHS
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