Question

prove that (sin A+cosec A)^2 + (cos A+secA)^2 =7+ tan^2 A + cot^2A.​

Answer 1

Step-by-step explanation:

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Answer 2

$\huge\boxed{Answer}$

Using Properties :-

Sin²A + Cos²A = 1

Cosec²A = 1 + Cot²A

Sec²A = 1 + tan²A

Solution :-

(SinA + CosecA)² + (CosA + SecA)²

=> (Sin²A + Cosec²A + 2SinA*CosecA) +

(Cos²A + Sec²A + 2CosA*SecA)

=> (Sin²A + Cosec²A + 2 + Cos²A + Sec²A + 2)

=> ( Sin²A + Cos²A + Cose²A + Sec²A + 4 )

=> 1 + (1 + Cot²A) + (1 + tan²A) + 4

=> 7 + tan²A + Cot²A

Hence Proof