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

Simplify each of the following:`cos^(-1)(3/5cosx+4/5sinx)`, where `-(3

1.	Simplify each of the following:`cos^(-1)(3/5cosx+4/5sinx)`, where `-(3pi)/4lt=xlt=pi/4`
Answer» `cos^-1 (3/5 cos x + 4/5 sin x)` here, `cos alpha= 3/5` `sin alpha = 4/5` so,`cos^-1[cos alpha cos x + sin alpha sin x]` `= cos^-1[ cos(x- alpha)]` `x- alpha` as`alpha = cos^-1 (3/5) = sin^-1(4/5) = tan^-1(4/3)` so,answer=`x- tan^-1 (4/3)`

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In a ` A B C ,`, if C is a right angle, then `tan^(-1)(a/(b+c))+tan^(-1)(b/(c+a))=``pi/3`(b) `pi/4`(c) `(5pi)/2`(d) `pi/6`
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