Question 63547
I'm not sure how to go about this one 
cos( tan-1(1/2) + tan-1(1/3))= I SAY  
Thanks
PUT 
TAN^(-1)[1/2]=X...HENCE 
TAN(X)=1/2..................1
LET
TAN^(-1)[3]=Y....HENCE 
TAN(Y)=1/3.........................2
WE HAVE 
I = COS(X+Y)=COS(X)COS(Y)-SIN(X)SIN(Y)
COS(X) = 1/SEC(X) = 1/SQRT[(1+TAN^2(X)]=1/SQRT[1+1/4]=2SQRT(5)/5
SIN(X) = 1/COSEC(X)=1/SQRT[1+COT^2(X)]=1/SQRT[1+{1/TAN^2(X)}]
=1/SQRT(5)=SQRT(5)/5
SIMILARLY 
COS(Y) = 3SQRT(10)/10
SIN(Y) = SQRT(10)/10
HENCE 
I = [2SQRT(5)*3SQRT(10)/(5*10)] - [SQRT(5)*SQRT(10)/(5*10)]
=[6SQRT(50)/50]-[SQRT(50)/50]=5SQRT(50)/50 =25SQRT(2)/50=SQRT(2)/2