Question

prove that (sinA+cosecA)^2+(cos A+secA)^2=7+tanA^2+cotA^2

Answer 1

namaste ✔.

(sinA + cosecA)² + (cosA + secA ) ²

sin²A + cosec²A + 2sinA×cosecA + cos²A + sec²A +2 cosA×secA

sin²A + cos²A + cose²cA +sec²A + 2sinA×1/sinA + 2cosA×1/cosA

•°• cosec²A = 1 + sec²A
and , sec²A = 1 + tan²A
hence ,
= 1 + 1 + cot²A + 1 + tan²A + 2 + 2

= 7 + tan²A + cot²A RHs prooved ...