If 8tanA=-15 and 25sinB=-7, Prove that SinA CosB + COSA SinB = -304/425
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Answer:
Consider the given data.
cosA=cosB=−
2
1
We know that cosine function is negative in second quadrant and third quadrant, so if A does not lie in 2nd quadrant, it must i.e. in 3rd quadrant $$ if B does not lie 3rd quadrant, it must lie in 2nd quadrant now, we have
cosA=−
2
1
cosA=−cos
3
π
⇒cos(π+
3
π
)
cosA=cos(
3
4π
)
A=
3
4π
Similarly,
cosB=−
2
1
cosB=−cos
3
π
⇒cos(π−
3
π
)
cosB=cos(
3
2π
)
B=
3
2π
Therefore,
sinA=sin
3
4π
=−
2
3
tanA=tan
3
4π
=
3
sinB=sin
3
2π
=
2
3
tanB=tan
3
2π
=−
3
Since,
tanB+sinA
4sinB−3tanA
=
−
3
−
2
3
4×
2
3
−3×
3
=
−
2
3
3
2
3
−3
3
=
−
2
3
3
−
3
=
3
2
Hence, the value is
3
2
.
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