Question

Given `cosx = -3/5` and `0<x<180`, what is `tan(x+45)`?

Answer 1

`tan(x+45)^@=1`

Explanation:

`"using the "color(blue)"trigonometric identities"`

`•color(white)(x)tanx=sinx/cosx`

`•color(white)(x)tan(x+y)=(tanx+tany)/(1-tanxtany)`

`•color(white)(x)sin^2x+cos^2x=1`

`rArrsinx=+-sqrt(1-cos^2x)`

`"cosx<0" and "0 < x < 180`

`rArr" x is in the second quadrant where "sinx>0`

`sinx=+sqrt(1-(-3/5)^2)`

`color(white)(sinx)=sqrt(1-9/25)=sqrt(16/25)=4/5`

`rArrtanx=4/5xx-5/3=-4/3`

`rArrtan(x+45)=(-4/3+1)/(1-4/3)=(-1/3)/(-1/3)=1`