If 2 \tan x+3 \cot x=5, then the value of 4 \tan ^{2} x+9 \cot ^{2} x is

SSC CHSL 12 Apr 2021 Shift 2 Paper

Section: Quantitative Aptitude

Question : 70 of 100

Marks: +1, -0

2 \tan x+3 \cot x=5

, then the value of

4 \tan ^{2} x+9 \cot ^{2} x

Solution:

Given,

2 \tan x+3 \cot x=5

On squaring both sides,

(2 \tan x+3 \cot x)^{2}=(5)^{2}

⇒ 4 \tan ^{2} x+9 \cot ^{2} x+2 × 2 \tan x

\;\; × 3 \cot x=25

⇒ 4 \tan ^{2} x+9 \cot ^{2} x+12=25

[ ∵ \tan x=\;{1}/{\cot x}]

∴ \tan ^{2} x+9 \cot ^{2} x=25-12=13 .

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