Question

1-2 cosec theta × cot theta + 2 cot² theta = cosec theta - cot theta / cosec theta + cot theta ​
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Answer 1

Answer:

Step-by-step explanation:

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