EXAMPLE 4. If sin 2A=2 sin 2B, then what is the
tan(A+B)
value of
-?
tan (A-B)
Answers
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0
Answer:
sin2A=λsin2B
RHS
=
λ−1
λ+1
=
sin2B
sin2A
−1
sin2B
sin2A
+1
=
sin2A−sin2B
sin2A+sin2B
=
2sin(
2
2A−2B
)cos(
2
2A+2B
)
2sin(
2
2A−2B
)cos(
2
2A−2B
)
=
sin(A−B)cos(A+B)
sin(A+B)cos(A−B)
=
tan(A−B)
tan(A+B)
=LHS
Hence proved.
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