Prove that:`sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi`

1.	Prove that:`sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi`
Answer» here, `alpha + beta + gamma = pi` `sin alpha = 12/13` so, `tan alpha = 12/5` and `cos beta = 4/5` so, `tan beta= 3/4` and `tan gamma = 63/16` so,`alpha + beta = pi -gamma` `tan(alpha + beta) = tan(pi- gamma)` `(tan alpha + tan beta)/(1 - tan beta) = (tan pi -tan gamma)/(1+ tan pi tan gamma) ` `= (12/5 + 3/4)/(1- 12/5 xx 3/4) = -(63/16)` `(48 + 15)/(-16) = -63/16` hence proved

Discussion

Prove that:`sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi`
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