In A le ABC, 5 cos A + 3 =0 then the quadratic equation whose roots are sinA and tan
with explanation
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5cosA+3=0
5cosA=−3
cosA=−
5
3
cosA is negative, so angle A is an obtuse angle.
∠A>90
∘
sinA=
1−cos
2
A
sinA=
1−(
5
−3
)
2
sinA=
25
16
=
5
4
( sinA will be positive because angle A lies in second quadrant )
tanA=
cosA
sinA
=−
3
4
If sinA and tanA are the roots of a quadratic equation, then the equation is,
x
2
−x(sinA+tanA)+(sinA⋅tanA)=0
x
2
−x(
5
4
−
3
4
)+(
5
4
×
3
−4
)=0
x
2
−x(
15
−8
)−(
15
16
)=0
15x
2
+8x−16=0
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