Question

(sinA+cosecA)squre+(cosA+secA)squre =tan squre A+cot squre A+7

Answer 1

Hey !!!

From LHS

(sinA + cosecA )² + (cosA + secA )²

•°• (a + b)² = a² + b² + 2ab
similarly ,

=> sin²A + cosec²A + 2sinA× cosA + cos²A + sec²A + 2 cosA× secA

=> sin²A + cosec²A + 2 × sinA × 1/sinA + cos²A + sec²A + 2 × cosA × 1/cosA

=> sin²A + cos²A + sec²A + cosec²A + 2 + 2

=> 1 + ( 1 + tan²A ) ( 1 + cot²A) + 4

=> 1 + 1 + 1 + 4 + tan²A + cot²A

=> 7 + tan²A + cot²A

tan²A + cot²A + 7

RHs = LHS prooved ♻

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Hope it helps you !!!

@Rajukumar111

Answer 2

Hope this helps you ☺