Question

prove that (sinA + cosecA )^2 +(cosA+secA)^2=7+tan^2A+cot^2A​

Answer 1

hope it is beneficial for you.....

Answer 2

LHS

=(sinA + cosecA)² + (cosA + secA)²

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

= (sin²A + cos²A) + cosec²A + sec²A + 2 + 2

= 1 + 4 + (cosec²A) + (sec²A)

= 5 + (cot²A + 1) + (tan²A + 1)

= 5 + 1 + 1 + tan²A + cot²A

= 7 + tan²A + cot²A

= RHS.

Hence proved.