Question

if sec square tita (1-sin tita)(1+sin tita)=k find the volu of k​

Answer 1

Given :

$\sf sec^2\theta(1-sin\theta)(1+sin\theta)=k$

To Find :

Value of k

Formula Applied :

$\bullet\ \; \sf (a+b)(a-b)=a^2-b^2$

$\bullet\ \; \sf sec\theta =\dfrac{1}{cos\theta}$

$\bullet\ \; \sf (1-sin^2\theta)=cos^2\theta$

Solution :

Take LHS

$\to \sf sec^2(1-sin\theta)(1+sin\theta)$

$\to \sf sec^2\theta(1^2-sin^2\theta)\\\\\to \sf sec^2\theta(1-sin^2\theta)$

$\to \sf sec^2\theta(cos^2\theta)$

$\to \sf \dfrac{1}{cos^2\theta}.cos^2\theta$

$\to \sf\ \; 1\ \; \bigstar$

So , k = 1