Question

(Sin 5A - sin3A)/(cos 3A +cos 5A)

Answer 1

Answer:

Given,

(Sin5A-Sin3A)/(Cos3A-Cos5A)

we know,

[SinC-SinD=2Sin(C+D/2)Cos(C-D/2)]

[CosC-CosD=-2Sin(C+D/2)Sin(C-D/2)]

so, by using these formula's we get....

=[2Cos{(5A+3A)/2}Sin{(5A-3A)/2}] /

[-2Sin{(3A+5A)/2}Sin{(3A-5A)/2}]

=[cos(8A/2)Sin(2A/2)]/[Sin(8A/2)Sin(-2A/2)]

=[Cos(4A)SinA]/[-Sin(4A)Sin(-A)

we know that Sin(-theta)=-Sintheta

=[Cos4ASinA]/[-Sin4A-SinA]

=[Cos4ASinA]/[Sin4ASinA]

=[Cos4A/Sin4A]

we know that, Cos(theta)/Sin(theta)=Cot(theta)

=Cot4A

it is the answer.

HOPE IT HELPS YOU .

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