show that (tan theta +2) (2 tan theta +1)= 5 tan theta + 2 sec^2 theta
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L.H.S.,
(Tan theta + 2)(2tan theta + 1)
= 2tan^2theta + tan theta + 4tan theta + 2
= 5tan theta + 2tan^2 theta + 2
= 5tan theta + 2 (tan^2 theta + 1)
= 5tan theta + 2 (sec^2 theta)
[Since, tan^2 theta + 1 = sec^2 theta]
= 5tan theta + 2sec^2 theta
= R.H.S.
Therefore, Proved.
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