`195^@ = 225^@ - 30^@` Find the exact values of the sine, cosine, and tangent of the angle.

Expert Answers
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`sin(u-v)=sin(u)cos(v)-cos(u)sin(v)`

`sin(225-30)=sin(225)cos(30)-cos(225)sin(30)`

`sin(225-30)=(-sqrt2/2)(sqrt3/2)-(-sqrt2/2)(1/2)=-sqrt2/4(sqrt3-1)`

 

`cos(u-v)=cos(u)cos(v)+sin(u)sin(v)`

`cos(225-30)=cos(225)cos(30)+sin(225)sin(30)`

`cos(225-30)=(-sqrt2/2)(sqrt3/2)+(-sqrt2/2)(1/2)=-sqrt2/4(sqrt3+1)`

 

`tan(u-v)=(tan(u)-tan(v))/(1+tan(u)tan(v))`

`tan(225-30)=(tan(225)-tan(30))/(1+tan(225)tan(30))=(1-(sqrt3/3))/(1+(1)(sqrt3/3))=(3-sqrt3)/(3+sqrt3)`

The rationalized answer is `2-sqrt3.`