Question

The derivation of tan inverse x with respect to cot inverse x is

Answer 1

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Answer 2

Concept:

Trigonometry is the relation between the angles of the triangle.

We can use trigonometric functions to find the length of the sides of the triangle.

Trigonometric functions are sine function, cosine functions,  tangent function, co-tangent function, secant function and co-secant function.

Given:

We are given that:

Tan⁻¹ x and cot⁻¹ x

Find:

We need to find that:

The derivation of tan inverse x with respect to cot inverse x.

Solution :

Let y= tan⁻¹ x

And z=cot⁻¹ x

Now, we will first differentiate y with respect to x.

Differentiating y with respect to x we get:

dy/dx=1/(1+x²)  ...(1)

Now, we will first differentiate z with respect to x.

Differentiating z with respect to x we get:

dz/dx=-1/(1+x²)   ...(2)

Now, we need dy/dz:

From (1) and (2), we get

dy/dz=(1/(1+x²) )/(-1/(1+x²))

dy/dz=-1

Therefore, we get that, the derivation of tan inverse x with respect to cot inverse x is -1.

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