If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.

Given:

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

$\Rightarrow \sec ^{2} \theta\{(1+\sin \theta)(1-\sin \theta)\}=k$

$\Rightarrow \quad \sec ^{2} \theta\left(1-\sin ^{2} \theta\right)=k$

$\Rightarrow \quad \sec ^{2} \theta \cos ^{2} \theta=k$

$\Rightarrow \quad \frac{1}{\cos ^{2} \theta} \times \cos ^{2} \theta=k$

$\Rightarrow \quad 1=k$

$\Rightarrow \quad k=1$

Hence, the value of k is 1.