# Prove each of the following. Use proper LHS/ RHS format for full marks. 1. cosθcotθ= 1/sinθ -sinθ 2. 1+cotθ/ cscθ = sinθ+ cosθ?

Any help, even if one question,would be much appreciated!

### 1 Answer

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- RayLv 66 years agoFavorite Answer
Here's the first as an example of the layout:

LHS = cosθcotθ

= cosθ * cosθ/sinθ ... because cotθ = 1/tanθ

= cos^2θ / sinθ

= (1 - sin^2θ)/sinθ ... using identity that cos^2θ + sin^2θ = 1

= 1/sinθ - sinθ = RHS

Proceed the same way with the other: convert cotθ and cosecθ into their equivalents in terms of sinθ and cosθ, and the simplification will become clear.

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