What is the value of cos `{"cos"^(-1)(4)/(5)+ "cos"^(-1)(12)/(13)}` ?

Options

A. 63/65
B. 33/65
C. 22/65
D. `11//65`

Answer

B

Explanation

Let `"cos"^(-1)(4)/(5)=A rArr cos A =(4)/(5)rArr sin A=(3)/(5)`
Let `"cos"^(-1)(12)/(13)=B rArr cos B =(12)/(13)rArr sin B=(5)/(13)`
Now, `cos("cos"^(-1)(4)/(5)+"cos"^(-1)(12)/(13))=cos(A+B)=cosA cosB - sinA sinB`
`=((4)/(5))((12)/(13))-((3)/(5))((5)/(13))=(33)/(65)`