Prove that ` sin ^(-1).(3)/(5) = tan ^(-1) .(3)/(4)`.

1.	Prove that ` sin ^(-1).(3)/(5) = tan ^(-1) .(3)/(4)`.
Answer» Let `sin ^(-1).(3)/(5) =theta` `rArr" "sin theta =(3)/(5) rArr cosec theta=(5)/(3)` `rArr " "cosec^(2) theta =(25)/(9) " "rArr 1 + cot^(2) theta=(25)/(9)` `rArr" "cot^(2)theta =(16)/(9) rArr " "cot theta =(4)/(3)` `rArr" "sin ^(-1).(3)/(5) = tan^(-1).(3)/(4)`

Discussion

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