Question

Question #cef51

Answer 1

See the solution below

Explanation:

L.H.S
`= tan^2(x) + cos^2(x) * 1/ (sec(x) + sin(x))`
`= sec^2(x) -1 + cos^2(x) * 1/ (sec(x) + sin(x))`

[since `color(blue)(tan^2(x) = sec^2(x)-1`)]

`= sec^2(x) -1 +1 - sin^2(x) * 1/(sec(x) + sin(x))`
`= sec^2(x) - sin^2(x) * 1/(sec(x) + sin(x))`
`= {sec(x) + sin(x)}{sec(x) - sin(x)}*1/(sec(x) + sin(x))`

simplifying we get as
`= sec(x) - sin(x) = R.H.S`