Question #cef51

1 Answer
Tony
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#

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