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prove the following result tan^-1(1/4) +tan^-1(2/9)=1/2 sin^-1(4/5)

prove the following result
tan^-1(1/4) +tan^-1(2/9)=1/2 sin^-1(4/5)

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago
tan-1(1/4)+tan-1(2/9)=tan-1(1/4+2/9)/(1-(1/4)(2/9))
=tan-1(1/2)
=(1/2). 2tan-1(1/2)
=(1/2). tan-1{(2.(1/2))(1-(1/2)2)}
=(1/2).tan-1(4/3)
=1/2 sin-1(4/5) by using the formula tan-1x=sin-1(x/sqrt(1-x2))

Thanks & Regards
Rinkoo Gupta
AskIITians faculty

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