Question

If cos (A + B) sin (C-D) = cos (A - B) sin (C+D), then show that
tan A tan B tan C + tan D=0.​

Answer 1

Answer:

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Step-by-step explanation:

cos(a+b) sin(c-d) = cos(a-b) sin(c+d)

( cosAcosB - sinAsinB) (sincCosD- cosC sinD) = ( cosAcosB + sinAsinB) (sincCosD+ cosC sinD)

- cosA cosBcosCsinD - sinA sinB sinC cosD = cosA cosB cosC sinD + sinA sinB sinC cosD

2 cosA cosBcosCsinD + 2sinA sinB sinC cosD=0

sinA sinB sinC cosD = - cosA cosBcosCsinD

tanA tanB tanC = - tanD

tannA tanB tanC + tanD =0

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