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!
- RayLv 65 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.