Question

If `cos(alpha+beta)=4/5; sin(alpha-beta)=5/13` and `alpha,beta` lie between `0&pi/4` then find the value of `tan2alpha`

Answer 1

Correct Answer - `(56)/(33)`
Since, `cos(alpha+beta)=(4)/(5)`
and `sin(alpha-beta)=(5)/(13)`
`therefore tan(alpha+beta)=(3)/(4)`
and `tan(alpha-beta)=(5)/(12)`
Now, `tan2alpha=tan[(alpha+beta)+(alpha-beta)]`
`=(tan(alpha+beta)+tan(alpha-beta))/(1-tan(alpha+beta).tan(alpha-beta))=((3)/(4)+(5)/(12))/(1-(3)/(4).(5)/(12))=(56)/(33)`