#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (i) (cosec θ - cot θ)^2 = (1-cos θ)/(1+cos θ)

Harshit Singh
8 months ago
Dear Student

(cosec θ-cot θ)^2= (1-cos θ)/(1+cos θ)
To prove this, first take the Left-Hand side (L.H.S) of the given equation, to prove the Right Hand Side (R.H.S)

L.H.S. = (cosec θ-cot θ)^2
The above equation is in the form of (a-b) , and expand it
Since (a-b)^2= a^2+ b^2–2ab
Here a = cosec θ and b = cot θ
= (cosec^2 θ +cot^2 θ-2cosec θ cot θ)
Now,
apply the corresponding inverse functions and equivalent ratios to simplify
= (1/sin^2 θ+ cos^2 θ/sin^2 θ-2cos θ/sin^2 θ)

= (1 + cos^2 θ-2cos θ)/(1 - cos^2 θ)

= (1-cos θ)^2 /(1 -cosθ)(1+cos θ)

= (1-cos θ)/(1+cos θ) =R.H.S.

Therefore,
(cosec θ-cot θ)^2= (1-cos θ)/(1+cos θ)
Hence proved.

Thanks