Question

prove that cos ^-1 (4/5) +tan^-1(3/5) = tan^-1 (27/11)​

Answer 1

Acc. to me,

your question,

L.H.S                                           R.H.S

cos^-1(4/5) +  tan^-1(3/5)  =   tan^-1(27/11)

First convert L.H.S into tan^-1  by triangle rule

then use formula  

tan^-1 x +tan^-1 y=tan^-1(x+y/1-xy)

so cos^-1(4/5)---change to tan^-1(3/4)

tan^-1(3/4) +  tan^-1(3/5)  =   tan^-1(27/11)

By formula

tan^-1 {(3/4 - 3/5)  /1 - (3/4*3/5)}

tan^-1{27/20  /  11/20}

tan^-1{27/11} -----proved

I hope you understand