Question

If sec^2 theta (1-sin theta) (1+sin theta)=k,find the value of k​

Answer 1

$\bf\large\red{\underline{\underline{Question}}}:$

• If sec^2 theta (1-sin theta) (1+sin theta)=k,find the value of k.

$\bf\large\red{\underline{\underline{Solution}}}:$

→ sec²θ (1-sin θ) (1+sinθ) = k

⇒ sec²θ (1²-sin²θ) = k            ∵ [(a-b)(a+b) = a²-b²]

⇒ sec²θ ( cos²θ ) = k

$\rm\implies \dfrac{1}{\cancel{\cos^2\theta}}\cancel{\cos^2\theta} = k$

⇒ 1 = k

Henceforth ,

• k = 1