prove that tan^-1(yz/xr) + tan^-1(zx/yr) + tan^-1(xy/zr) = pie/2 where, x^2 + y^2 + z^2 = r^2 - Maths - Inverse Trigonometric Functions

Question

prove that tan^-1(yz/xr) + tan^-1(zx/yr) + tan^-1(xy/zr) = pie/2
where, x^2 + y^2 + z^2 = r^2

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

To Prove :-tan-1yzxr+tan-1zxyr+tan-1xyzr=π2LHStan-1yzxr+tan-1zxyr+tan-1xyzr=tan-1yzxr+zxyr1-yzxrzxyr+tan-1xyzr=tan-1y2z+zx2xyrxyr2-xyz2xyr2+tan-1xyzr=tan-1rz x2+y2xy r2-z2+tan-1xyzr=tan-1 rz x2+y2xy r2-z2+xyzr1-rz x2+y2xy r2-z2xyzr=tan-1 rz x2+y2xy r2-z2+xyzr1-x2+y2r2-z2=tan-1 rz x2+y2xy r2-z2+xyzrr2-z2-x2-y2r2-z2=tan-1 rz x2+y2xy r2-z2+xyzrr2-z2+x2+y2r2-z2=tan-1 rz x2+y2xy r2-z2+xyzrr2-r2r2-z2=tan-1 rz x2+y2xy r2-z2+xyzr0=π2=RHSHence Proved 
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