Solve for x , where 0 degree ≤X ≤90 degree
Sin2x + Cos230 = 5/4
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Maths
If 0
∘
<x<90
∘
and 2sinx+15cos
2
x=7, then what is the value of tanx?
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Correct option is
C
3
4
2sinx+15cos
2
x=7
2sinx+15(1−sin
2
x)−7=0
2sinx−15sin
2
x+8=0
15sin
2
x−2sinx−8=0
sinx=
2.15
2±
4+4.15.8
=
30
2±
4+480
=
30
2±22
=
30
24
,
30
−20
sinx>0 (∵0<x<90
o
)
sinx=
30
24
=
5
4
cosx=
1−
25
16
=
25
9
=
5
3
tanx=
cosx
sinx
=
3/5
4/5
=
3
4
∴tanx=
3
4
.
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