If cos(A+B)=52, cosAcosB=43, then the value of tanAtanB=....
Explanation
Recall the cosine addition concept
cos(A+B)=cosAcosB−sinAsinB
Finding sin A sin B
Substitute the given values into the cosine addition formula.
cos(A+B)=52
cosAcosB−sinAsinB=52
43−sinAsinB=52
sinAsinB=207
Finding tan A tan B
Recall that tanA=cosAsinA, then
tanAtanB=cosAcosBsinAsinB
tanAtanB=43207
tanAtanB=207×34
tanAtanB=157
Therefore, the value of tanAtanB is 157.