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Question

If 2secθ+3tanθ=7(0<θ<90), then the value of
2tanθ+3secθ is

A
23
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B
36
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C
7
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D
17
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Solution

The correct option is B 36
Let 2tanθ+3secθ=x
2secθ+3tanθ=7 .......(1)
3secθ+2tanθ=x .......(2)
3×eqn(1)2×eqn(2) we get
6secθ+9tanθ6secθ4tanθ=212x
5tanθ=212x
tanθ=212x5 ........(3)
2×eqn(1)3×eqn(2) we get
4secθ+6tanθ9secθ6tanθ=143x
5secθ=143x
secθ=143x5 .......(4)
We know that sec2θtan2θ=1 .......(5)
Substituting (3) and (4) in (5) we get
(143x5)2(212x5)2=1
(143x)2+(212x)2=25
(143x21+2x)(143x+212x)=25
(x7)(5x+35)=25
(x+7)(5)(x7)=25
x249=5
x2=5+49=54
x=36

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