express 2sin61°*sin39° as sum or difference form
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Answer:
Consider the equation,
Case 1- 2sin4θcos2θ
sinA+sinB=2sin(
2
A+B
)cos(
2
A−B
)
=2sin(
2
6θ+2θ
)cos(
2
6θ−2θ
)
=2sin4θcos2θ
Case 2- 2sin2θcos4θ
sinA+sinB=2sin(
2
A+B
)cos(
2
A−B
)
=2cos(
2
6θ+2θ
)sin(
2
6θ−2θ
)
Case 3- 2sin2θsin4θ
cosA−cosB=−2sin(
2
A+B
)sin(
2
A−B
)
=−2sin(
2
6θ+4θ
)sin(
2
6θ−2θ
)
=2sin2θsin4θ
Case 4-2cos2θcos4θ
cosA−cosB=2cos(
2
A+B
)cos(
2
A−B
)
=2cos(
2
6θ+4θ
)cos(
2
6θ−4θ
)
=2cos2θcos4θ
Hence, Proved.
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