Question

Prove it,

sec²x + cosec²x = sec²x cosec²x

Answer 1

LHS = Sec²x + cosec²x

$= \frac{1}{cos {}^{2}x } + \frac{1}{ {sin}^{2}x } \\ \\ = \frac{ {sin}^{2}x + cos {}^{2}x }{ {cos}^{2} x \times {sin}^{2} x} \\ \\ = \frac{1}{ {cos}^{2}x \times {sin}^{2}x } \\ \\ = {sec}^{2} x. {cosec}^{2} x$




LHS = RHS

Answer 2

L. H. S = sec²x + cosec²x

( 1 / Cos ²x ) + ( 1 / sin²x )

=> ( Sin ²x + Cos²x ) / Cos ²x sin ²x

=> 1 / cos²x sin²x

=> sec ²x cosec ²x

=> R. H. S.

[ 1 / Cos²x = sec ²x, 1 / sin ²x = cosec ²x ].

HENCE, PROVED.