Simplify each of the following: `cos^(-1)(3/5cosx+4/5sinx)` , where `-(3pi)/4lt=xlt=pi/4` `sin^(-1)(5/(13)cosx+(12)/(13)sinx)`

Answer

N/a

Explanation

We have, `cos^(-1)[3/5cosx+4/5sinx],x in [(-3pi)/4, pi/4]`
Let `cosy = 3/5`
`rArr sin y = 4/5`
`rArr y = cos^(-1)'3/5=sin^(-1)'4/5=tan^(-1)'(4/3)`
`cos^(-1)[cosy.cosx+siny.sinx]`
`=cos^(-1) [cos(y-x)], [:'cos(A-B)=cosA.cosB+sinA.sinB]`
`= y - x = tan^(-1)'4/3-x` , `[:' y = tan^(-1) '4/3]`