Question

Use the fundamental identities to verify the following: 1- (sin^2 theta)/1- cos theta = -cos theta

Answer 1

For convenience : \(\cfrac{1- \sin^2 \theta } { 1- \cos \theta } \)

Answer 2

Use identity : \(1 - \sin^2 \theta = \cos \theta \)

So you get : \(\cfrac{ \cos \theta }{ 1 - \cos \theta} = -\cos \theta \)

Can you cancel out \(\cos \theta \) which is present on RHS and LHS in the numerators... ?

Answer 3

Though, I doubt that I have taken the question incorrect or the question, itself is incorrect...

Is it : \(1 - \cfrac{\sin^2 \theta}{1-\cos \theta} = - \cos \theta\) or \(\cfrac{1-\sin^2\theta}{1-\cos\theta}= -\cos\theta\) ? \

Answer 4

I think, it should be the first one...

You can solve it by the following way :

1 + cos theta = \(\cfrac{\sin^2 \theta}{1-\cos \theta} \)

(1+ cos theta)(1-cos theta) = sin^2 theta

Use dientity : 1 - cos^2 theta = sin^2 theta

therefore 1 - cos^2 theta = sin^2 theta = sin^2 theta

verified...