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Proof that (sinA cosA)(1-sinAcosA)=tan²A cot²A+7?
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Proof that (sinA cosA)(1-sinAcosA)=tan²A cot²A+7?
Ans.

Method to solve :   

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

LHS = (sinA + cosecA)� + (cosA + secA)�
= (sin�A + 2*sinA*cosecA + cosec�A) + (cos�A + 2*cosA*secA + sec�A)
= (sin�A + cos�A) + (cosec�A + sec�A) + (2*sinA*cosecA + 2*cosA*secA)
= 1 + (1 + cot�A) + (1 + tan�A) + (2 + 2) … {sin�A + cos�A = 1, cosec�A = 1 + cot�A, sec�A = 1 + tan�A, sinA*cosecA = 1, cosA*secA = 1}
= 7 + tan�A + cot�A = RHS

 (sinA + cosecA)� + (cosA + secA)� = 7 + tan�A + cot�A
 
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Proof that (sinA cosA)(1-sinAcosA)=tan²A cot²A+7?
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