Question

cosec theta + cot theta upon cosec theta minus cot theta is equal to 1 + 2 cos square theta + 2 cos square theta cos theta ​

Answer 1

Answer:

Consider L.H.S = cosecθ + cotθ/cosecθ - cotθ

Multiplying and dividing by cosecθ + cotθ, we get

= (cosecθ + cotθ)²/(cosecθ - cotθ)(cosecθ + cotθ)

We know that (cosecθ - cotθ)(cosecθ + cotθ) = cosec²θ - cot²θ

But we know that cosec²θ - cot²θ = 1

So, L.H.S

= (cosecθ + cotθ)²/1

= cosec²θ + cot²θ + 2cosecθcotθ

We can write cosec²θ = 1 + cot²θ

So, L.H.S

= 1 + cot²θ + cot²θ + 2cosecθcotθ

= 1 + 2cot²θ + 2cosecθcotθ

= R.H.S

Hence , Proved

Answer 2

Answer:

Hope this will help you