Question

prove that cos-1(5/13)=tan-1(12/5)​

Answer 1

Given, cos-1 (5/13) = tan-1 (12/5)

Given, cos-1 (5/13) = tan-1 (12/5)=> tan-1 [√{1 - (5/13)2 }/(5/13)] = tan-1 (12/5) [ since cos-1 x = tan-1 {√(1 - x)2 /x} ]

Given, cos-1 (5/13) = tan-1 (12/5)=> tan-1 [√{1 - (5/13)2 }/(5/13)] = tan-1 (12/5) [ since cos-1 x = tan-1 {√(1 - x)2 /x} ]=> tan-1 [√{1 - 25/169}/(5/13)] = tan-1 (12/5)

Given, cos-1 (5/13) = tan-1 (12/5)=> tan-1 [√{1 - (5/13)2 }/(5/13)] = tan-1 (12/5) [ since cos-1 x = tan-1 {√(1 - x)2 /x} ]=> tan-1 [√{1 - 25/169}/(5/13)] = tan-1 (12/5)=> tan-1 [√{(169 - 25)/169}/(5/13)] = tan-1 (12/5)

Given, cos-1 (5/13) = tan-1 (12/5)=> tan-1 [√{1 - (5/13)2 }/(5/13)] = tan-1 (12/5) [ since cos-1 x = tan-1 {√(1 - x)2 /x} ]=> tan-1 [√{1 - 25/169}/(5/13)] = tan-1 (12/5)=> tan-1 [√{(169 - 25)/169}/(5/13)] = tan-1 (12/5)=> tan-1 [√{144/169}/(5/13)] = tan-1 (12/5)

Given, cos-1 (5/13) = tan-1 (12/5)=> tan-1 [√{1 - (5/13)2 }/(5/13)] = tan-1 (12/5) [ since cos-1 x = tan-1 {√(1 - x)2 /x} ]=> tan-1 [√{1 - 25/169}/(5/13)] = tan-1 (12/5)=> tan-1 [√{(169 - 25)/169}/(5/13)] = tan-1 (12/5)=> tan-1 [√{144/169}/(5/13)] = tan-1 (12/5)=> tan-1 [(12/13)/(5/13)] = tan-1 (12/5)

Given, cos-1 (5/13) = tan-1 (12/5)=> tan-1 [√{1 - (5/13)2 }/(5/13)] = tan-1 (12/5) [ since cos-1 x = tan-1 {√(1 - x)2 /x} ]=> tan-1 [√{1 - 25/169}/(5/13)] = tan-1 (12/5)=> tan-1 [√{(169 - 25)/169}/(5/13)] = tan-1 (12/5)=> tan-1 [√{144/169}/(5/13)] = tan-1 (12/5)=> tan-1 [(12/13)/(5/13)] = tan-1 (12/5)=> tan-1 (12/5) = tan-1 (12/5)

Given, cos-1 (5/13) = tan-1 (12/5)=> tan-1 [√{1 - (5/13)2 }/(5/13)] = tan-1 (12/5) [ since cos-1 x = tan-1 {√(1 - x)2 /x} ]=> tan-1 [√{1 - 25/169}/(5/13)] = tan-1 (12/5)=> tan-1 [√{(169 - 25)/169}/(5/13)] = tan-1 (12/5)=> tan-1 [√{144/169}/(5/13)] = tan-1 (12/5)=> tan-1 [(12/13)/(5/13)] = tan-1 (12/5)=> tan-1 (12/5) = tan-1 (12/5)So, cos-1 (5/13) = tan-1 (12/5)

Follow me dear for your future doubts ❤️❤️

Answer 2

hxigxigsgxgkgxbkgkcoyxohxhok hkxhox