CBSE Class 10CBSE
Share
Notifications

View all notifications

If secθ + tanθ = p, show that (p^2−1)/(p^2+1)=sinθ - CBSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`

Solution

We have,

`=(\sec ^{2}\theta +\tan ^{2}\theta +2\sec \theta \tan\theta -1)/(\sec ^{2}\theta +\tan^{2}\theta +2\sec \theta \tan\theta +1)`

`=\frac{(\sec ^{2}\theta -1)+\tan ^{2}\theta +2\sec \theta \tan\theta }{\sec ^{2}\theta +2\sec \theta \tan \theta +(1+\tan^{2}\theta )`

`=(\tan ^{2}\theta +\tan ^{2}\theta +2\sec \theta \tan\theta )/(\sec ^{2}\theta +2\sec \theta \tan \theta +\sec^{2}\theta )`

`=\frac{2\tan ^{2}\theta +2\tan \theta \sec \theta }{2\sec^{2}\theta +2\sec \theta \tan \theta }`

`=\frac{2\tan \theta (\tan \theta +\sec \theta )}{2\sec \theta (\sec\theta +\tan \theta )}`

`=\frac{\tan \theta }{\sec \theta }=\frac{\sin \theta }{\cos \theta \sec\theta }`

= sinθ = RHS

  Is there an error in this question or solution?
Solution If secθ + tanθ = p, show that (p^2−1)/(p^2+1)=sinθ Concept: Trigonometric Identities.
S
View in app×