Simplify 1+cot^2x | 1+cot^2x Formula [in terms of cosec]

The simplification or the formula of 1+cot2x is given as follows:

1+cot2x = cosec2x.

In this post, we will learn how to establish the formula of 1+cot2x.

1+cot^2x formula

Proof of 1+cot2x Formula

Question: Prove the formula 1+cot2x = cosec2x.


L.H.S. = 1+cot2x

= $1+(\dfrac{\cos x}{\sin x})^2$ as cotx=cosx/sinx.

= $1+\dfrac{\cos^2 x}{\sin^2 x}$

= $\dfrac{\sin^2 x + \cos^2 x}{\sin^2 x}$

= $\dfrac{1}{\sin^2 x}$ as we know that sin2x+cos2x=1.

= $(\dfrac{1}{\sin x})^2$

= cosec2x [∵ cosecx = 1/sinx]

= R.H.S.

So we have proven the formula of 1+cot2x in terms of cosec which is given by 1+cot2x = cosec2x.


Question: Find the value of 1+cot245.


In the above formula of 1+cot2x = cosec2x, we put x=45 degrees. So we get that

1+cot245 = cosec245 = (2)2 = 2.

So the value of 1+cot245 is equal to 2.


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Q1: What is the formula of 1+cot2x?

Answer: The formula of 1+cot2x is equal to 1+cot2x=cosec2x.

Q2: What is the formula of 1+cot2θ?

Answer: The formula of 1+cot2θ is equal to 1+cot2θ=cosec2θ.

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