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If tan(a-b)/tan a+sin²c/sin²a=1,show that tana.tanb=tan²c

1 Answers

taking the denominator common

the given sum can be written as

sin²acasbcosa-cos²sinbsina+sin²csinasinb++sin²ccosacosb=sin²csinasinb+sin²asinasinb

and cacelling out gives u

sin²ccosacosb=sinasinbcos²c

which gives tanatanb=tan²c

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