InterviewSolution
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InterviewSolution
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Prove that:`tan^(-1)(63/16)=sin^(-1)(5/13)+cos^(-1)(3/5)` |
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Answer» `R.H.S -> sin^-1(5/13)+cos^-1(3/5)` We can create two triangles with angle `theta` and `phi` as expalined in video. In that case, `sin^-1(5/13)` can be written as `tan^-1(5/12)` `cos^-1(3/5)` can be wriiten as `tan^-1(4/3)` So, we can rewrite R.H.S. as `tan^-1(5/12)+tan^-1(4/3)`As, `tan^-1x+tan^-1y = tan^-1((x+y)/(1-xy))`, above can be wtitten as `tan^-1(5/12+4/3)/(1-5/12**4/3)` `=tan^-1((7/4)/(4/9)) = tan^-1(63/16) = L.H.S.` |
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