If 3\sin x+4\cos x=5, then 6\tan x/2-9 \tan^2 x/2

NIMCET 2020 Question Paper with solutions

Question : 49 of 120

Marks: +1, -0

3\sin x+4\cos x=5

, then

6\tan x/2-9 \tan^2 x/2

Solution:

{3(2\tan x/2)}/{1+\tan^2x/2}+{4(1-\tan^2x/2)}/{1+\tan^2x/2}=5

Let

\tan x/2=t

⇒{6t}/{1+t^2}+{4(1-t^2)}/{1+t^2}=5

⇒6t-9t^2=1

⇒9t^2-6t+1=0

⇒t=1/3

⇒\tan x/2=1/3

⇒Therefore

6\tan x/2-9\tan^2x/2=1

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