Question

(1-cos² theta) (1+ tan² theta) = tan² theta​

Answer 1

Answer:

Here,

(1-cos2theta)(1-tan2theta)

Sin2theta *Sec2theta

Sin2theta*1/cos2theta

So,,sin 2theta/cos2theta

_______tan2theta_______

Hope it will be helpful

Step-by-step explanation:

Answer 2

Given:-

$(1-cos^2 \theta) (1+ tan^2 \theta)$

To prove :-

$tan^2 \theta$

Solution:-

We have Some Trignometric identities which helps to solve this problem:-

★ $\boxed{\sf{Sin^2 \theta = 1-cos^2 \theta}}$

★ $\boxed{\sf{Sec^2 \theta = 1 + tan^2 \theta}}$

Now, put their values :-

→ $(1-cos^2 \theta) (1+ tan^2 \theta)$

→$Sin^2 \theta . Sec^2 \theta$

→$Sin^2 \theta . \dfrac{1}{Cos^2\theta }$

→$\dfrac{Sin^2\theta }{Cos^2\theta }$

→$tan^2 \theta$

hence, (1-cos² theta) (1+ tan² theta) = tan² theta

proved....