Question

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

Answer 1

sec^2 theta (1+sin thata ) ( 2- sin theta ) = sec ^2 theta ( 1-sin theta) (a+b) (a-b) = (a^2 - b^2) =sec^2 theta .cos ^2 theta =1. ( cos sq. theta + sin sq theta =1) k=1

Answer 2

Given,

sec²θ (1+sinθ)(1-sinθ) = k

To find,

The final value of k.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Simplifying using trigonometric formula :

sec²θ (1+sinθ)(1-sinθ) = k

k = sec²θ (1+sinθ)(1-sinθ)

k = sec²θ {(1)²-(sinθ)²} [As, a²-b² = (a+b)(a-b)]

k = sec²θ (1-sin²θ)

k = sec²θ × cos²θ [As sin²θ+cos ²θ = 1, 1-cos²θ = sin²θ]

k = 1/cos²θ × cos²θ

k = 1

[We cannot simplify this further, so we will take this as our final result.]

Hence, the value of k will be 1.