Question

(1) tan A + cot A = sec A cosec A​

Answer 1

Step-by-step explanation:

taking LHS

tanA + cotA

sinA/cosA + cosA / sinA

sin^2A +cos^2A/ sinA cosA

1/ sinA cosA ; 1/sinA = cosecA, 1/ cosA = secA

secA cosecA

hence proved

Answer 2

$\tan(A) + \cot(A) = \sec(A) \csc(A)$

$\tan(A) + \dfrac{1}{\tan(A)} = \sec(A) \csc(A)$

$\dfrac{\tan ^{2} (A) + 1}{\tan(A)} = \sec(A) \csc(A)$

$\dfrac{ \sec ^{2} (A) }{ \tan(A) } = \sec(A) \csc(A)$

$\sec(A) \times \dfrac{ \sec(A) }{ \tan(A) } = \sec(A) \csc(A)$

$\sec(A) \csc(A) = \sec(A) \csc(A)$

Hence, Proved.