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If sin(alpha+beta)sin(alpha-beta)=singam...

If `sin(alpha+beta)sin(alpha-beta)=singamma(2sinbeta+singamma),` where `0

A

(1,1)

B

(-1,1)

C

(1,-1)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`"sin"(alpha+beta)"sin"(alpha-beta)="sin" gamma(2"sin"beta + "sin"gamma)`
`"or ""sin"^(2)alpha-("sin"beta + "sin" gamma)^(2)=0`
`"or "("sin"alpha+"sin" beta+"sin"gamma)("sin"alpha-"sin"beta-"sin"gamma)=0`
`"Since " 0 lt alpha, beta, gamma lt pi," we have"`
`"sin"alpha+"sin"beta+"sin"gamma ne 0`
`therefore " sin"alpha-"sin"beta-"sin"gamma = 0`
`"So, "x"sin" alpha+y"sin" beta-"sin"gamma=0` passes through the fixed point (1,-1).
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