Question

Prove that (sin A +cosec A)square+(cos A+sec A)square=7+tan square A+cot square A

Answer 1

see the attachment for your answer

Answer 2

$\huge\mathfrak{Heya}$

$\mathsf{See \ the \ attachement.}$

$\mathsf{Identities \ used \ :-}$

$\mathsf{1. \ (a + b)^2 \ = \ a^2 + b^2 + 2ab}$

$\mathsf{2. \ cosec^2A \ = \ 1 + cot^2A}$

$\mathsf{3. \ sec^2A \ = \ 1 + tan^2A}$

$\mathsf{4. \ sin^2A + cos^2A \ = \ 1}$

$\mathsf{5. \ cosec A}$ = $\frac{1}{sin A}$

$\mathsf{6. \ sec A}$= $\frac{1}{cos A}$

$\huge\mathbb{Hope \ this \ helps.}$