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Question
Prove that:
`tan^(-1) 63/16 = sin^(-1) 5/13 + cos^(-1) 3/5`
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Solution
Let `sin^(-1) 5/13` = x and `cos^(-1) 3/5` = y
⇒ sin x = `5/13 ` and cos y = `3/5`
or tan x = `5/12` and tan y = `4/3`
⇒ x = `tan^-1 5/12` and y = `tan^(-1) 4/3`
x + y = `tan^-1 5/12 + tan^-1 4/3`
= `tan^-1 ((5/12 + 4/3)/(1 - 5/12 xx 4/3))`
= `tan^(-1) ((15+48)/(36-20))`
= `tan^(-1) 63/16`
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