Question

(sinA+cosecA)^2 + (cosA + secA)^2

Answer 1

→ (SinA + CosecA)² + (CosA + SecA)²

→ (SinA + 1/SinA)² + (CosA + 1/CosA)²

→ (Sin²A + 1/Sin²A + 2) + (Cos²A + 1/Cos²A + 2)

→ 1 + 4 + (Sin²A+Cos²A)/Sin²ACos²A

→ 5 + 1/sin²ACos²A

Hope it helps :)

Answer 2

$\huge\mathtt\pink{Answer}$

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=(sinA+cosecA)²+(cosA+secA)²

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

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

=1+cosec²A+sec²A+2+2

=5+(1+cot²A)+(1+tan²A)

=7+tan²A+cot²A

Identities used:

1+tan²A=sec²A

1+cot²A=cosec²A

sin²A+cos²A=1

cosecA=1/sinA

secA=1/cosA

i hope it will help you !!