08:Write the function in the simplest form:cos x-sinxtan0<x<TTcOS X +

1.	08:Write the function in the simplest form:cos x-sinxtan0<x<TTcOS X + sin x
Answer» Let's multiply the numerator and denominator by cos(π/4)=sin(π/4): tan^−1(sin(π/4)cos(x)−cos(π/4)sin(x))/ (cos(π/4)cos(x)+sin(π/4)sin(x)), 0<x<π = tan^−1(sin(π/4−x)/ (cos(π/4−x)), 0<x<π = { π/4−x if 0<x<3π/4 not defined if x=3π/4 5π/4−x if 3π/4<x<π}

08:Write the function in the simplest form:cos x-sinxtan0<x<TTcOS X + sin x

Answer»

Let's multiply the numerator and denominator by cos(π/4)=sin(π/4):

tan^−1(sin(π/4)cos(x)−cos(π/4)sin(x))/ (cos(π/4)cos(x)+sin(π/4)sin(x)), 0<x<π

= tan^−1(sin(π/4−x)/ (cos(π/4−x)), 0<x<π

= { π/4−x if 0<x<3π/4 not defined if x=3π/4 5π/4−x if 3π/4<x<π}