Question

PLEASE DO IT IN NOTEBOOK​

Answer 1

Solution

To Prove:-

• (1 + tan² θ)( 1 + sin θ)( 1 - sin θ) = 1.

Prove:-

Take L.H.S.

= (1 + tan² θ)( 1 + sin θ)( 1 - sin θ)

Some of Important Formula

$\boxed{\tt{\:\tan\theta\:=\:\dfrac{\sin\theta}{\cos\theta}}}$

$\boxed{\tt{\:(1-\sin^2\theta)\:=\:\cos^2\theta}}$

So,Now

= (1 + tan² θ)( 1² - sin² θ)

= ( 1 + tan² θ) ( 1 - sin² θ)

Keep,

• ( 1 - sin² θ) = cos² θ.

= (1 + tan² θ)(cos² θ)

Now, keep

• tan θ = sin θ/cos θ.

So, Now

= (1 + sin² θ/cos² θ) × (cos² θ)

= [( cos² θ + sin² θ)/cos² θ] × cos² θ

We Know,

• cos² θ + sin² θ = 1.

= (1/cos² θ ) × cos²θ

= 1

R.H.S.

That's proved.

____________________

Answer 2

Solution

To Prove:-

(1 + tan² θ)( 1 + sin θ)( 1 - sin θ) = 1.

Prove:-

Take L.H.S.

= (1 + tan² θ)( 1 + sin θ)( 1 - sin θ)

Some of Important Formula

\boxed{\tt{\:\tan\theta\:=\:\dfrac{\sin\theta}{\cos\theta}}}

tanθ=

cosθ

sinθ

\boxed{\tt{\:(1-\sin^2\theta)\:=\:\cos^2\theta}}

(1−sin

2

θ)=cos

2

θ

So,Now

= (1 + tan² θ)( 1² - sin² θ)

= ( 1 + tan² θ) ( 1 - sin² θ)

Keep,

( 1 - sin² θ) = cos² θ.

= (1 + tan² θ)(cos² θ)

Now, keep

tan θ = sin θ/cos θ.

So, Now

= (1 + sin² θ/cos² θ) × (cos² θ)

= [( cos² θ + sin² θ)/cos² θ] × cos² θ

We Know,

cos² θ + sin² θ = 1.

= (1/cos² θ ) × cos²θ

= 1

R.H.S.

That's proved.

$\color{pink}{THANK YOU!}$