Advertisement Remove all ads

Prove the Following Trigonometric Identities. (Tan^2 A)/(1 + Tan^2 A) + (Cot^2 A)/(1 + Cot^2 A) = 1 - Mathematics

Prove the following trigonometric identities.

`(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`

Advertisement Remove all ads

Solution

In the given question, we need to prove `(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`

Here, we will first solve the LHS.

Now using `tan theta = sin theta/cos theta` and `cot theta = cos theta/sin theta` we get

`tan^2 A/(1 + tan^2 A) + cot^2 A/(1 + cot^2 A) = ((sin^2 A/cos^2 A))/((1 + sin^2 A/cos^2 A)) + ((cos^2 A/sin^2 A))/((1 + cos^2 A/sin^2 A))`

`= ((sin^2 A/cos^2 A))/(((cos^2 + sin^2 A)/cos^2 A)) + ((cos^2 A/sin^2 A))/(((sin^2 A + cos^2 A)/sin^2 A))`

`= ((sin^2 A/cos^2 A))/((1/cos^2 A)) + ((cos^2 A/sin^2 A))/((1/(sin^2  A)))`    (using `sin^2 theta + cos^2 theta = 1`)

On further solving by taking the reciprocal of the denominator, we get,

`(sin^2 A/cos^2 A)/(1/cos^2 A) + (cos^2 A/sin^2 A)/(1/sin^2 A) = ((sin^2 A)/(cos^2 A)) (cos^2 A/1) + (cos^2 A/sin^2 A)(sin^2 A/1)`

`= sin^2 A + cos^2 A`        (Using `sin^2 theta + cos^2 theta = 1`)

= 1

Hence proved.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 45 | Page 45
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×