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prove that tan⁻¹(1/4)+tan⁻¹(2/9)=1/2cos⁻¹(3/5)

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prove that tan⁻¹(1/4)+tan⁻¹(2/9)=1/2cos⁻¹(3/5)

Posted by Sudhanshu Tiwari 4 years, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Jerry Singh 4 years, 3 months ago

LHS=tan^-1(1/4)+tan^-1(2/9). =tan^-1[(1/4+12/9)/{1-(1/4)*(2/9)}] =tan^-1(17/34)=tan^-1(1/2). =1/2{2tan^-1(1/2)}. =1/2 cos^-1[{1-(1/4)}/{1+(1/4)}]. =1/2 cos^-1(3/5)=RHS

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