Question

prove that (sinA +cosecA)+(cosA+secA) = 7+ tan²a+cot²A.

Answer 1

Hey friend here is your answer

Pls refer to the attachment

Answer 2

$\bf\huge LHS = (sinA + cosecA)^2 + (cosA + secA)^2$

$\bf\huge (sin^2 A + cosec^2 A + 2sinA cosecA ) + (cos^2 A + sec^2 A + 2 cosA SecA)$

$\bf\huge (sin^2 A + cosec^2 A + 2 sinA . \frac{1}{sinA}) + (cos^2A + sec^2 A + 2 cosA . \frac{1}{cosA})$

$\bf\huge (sin^2 A + cosec^2 A + 2) + (cos^2 A + sec^2 A + 2)$

$\bf\huge (sin^2 A + cos^2 A + 2) + (cos^2 A + sec^2 A + 2)$

$\bf\huge sin^2 A + cos^2 A + cosec^2 A + sec^2 A + 4$

$\bf\huge 1 + (1 + cot^2) + (1 + tan^2 A) + 4$

$\bf\huge 7 + tan^2 A + cot^2 A$