Question

i need this answer please explain me ​

Answer 1

Solution

To Prove:-

• Sin (90° - θ)/(1 + sin θ) + cos θ/(1 - cos (90° - θ)) = 2 sec θ

Prove:-

Take L.H.S.

= Sin (90° - θ)/(1 + sin θ) + cos θ/(1 - cos( 90° - θ)

We Know,

★ sin (90° - θ) = cos θ

★ cos (90° - θ) = sin θ

Now, keep all above Values,

= cos θ/(1 + sin θ) + cos θ/(1 - sin θ)

= [cos θ( 1 - sin θ) + cos θ( 1 + sin θ)]/( 1² - sin² θ)

Take common cos θ

= cos θ[ 1 - sin θ + 1 + sin θ]/( 1 - sin² θ)

We Know,

★ ( 1 - sin² θ) = cos² θ

= 2 cos θ/cos² θ

= 2/cos θ

Keep here,

★ 1/cos θ = sec θ

= 2 sec θ

= R.H.S.

That's Proved.

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