Question

pls answer this question question no.9​

Answer 1

Step-by-step explanation:

9.

Given :-

Sec² θ ( 1+ Sin θ)(1- Sin θ)

To find :-

Find the value of Sec² θ ( 1+ Sin θ)(1- Sin θ) ?

Solution :-

Given that

Sec² θ ( 1+ Sin θ)(1- Sin θ)

=> Sec²θ(1²- Sin² θ)

Since (a+b)(a-b) = a²-b²

Where a = 1 and b = Sin θ

=> Sec² θ(1- Sin² θ)

We know that

Sin² A + Cos² A = 1

=> Sec² θ ( Cos² θ)

We know that

Sec A = 1/Cos A

=> (1/Cos² θ)(Cos² θ)

=> Cos² θ / Cos² θ

=> 1

Answer :-

The value of Sec² θ ( 1+ Sin θ)(1- Sin θ) is 1