Question #cef51

1 Answer
Aug 19, 2017

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