Question

if tan theta+sec theta =x then show that sin theta = x^2-1/

Answer 1

Answer:

the above is the answer

Answer 2

given

$sec \theta + tan \theta = x$

Now RHS

$\frac{ {x}^{2} - 1}{ {x}^{2} + 1 } \\ \\ = \frac{ {sec}^{2} \theta + {tan}^{2} \theta + 2sec \theta tan \theta - 1}{ {sec}^{2} \theta + {tan}^{2} \theta + 2sec \theta tan \theta + 1 } \\ \\ = \frac{2 {tan}^{2} \theta + 2sec \theta tan \theta }{2 {sec}^{2} \theta + 2sec \theta tan \theta } \\ \\ = \frac{tan \theta}{sec \theta} \\ \\ = sin \theta$