How do you write the expression as the sine, cosine, or tangent of the angle given #cos45^circcos120^circ-sin45^circsin120^circ#?

2 Answers
Aug 11, 2018

#cos165^@#

Explanation:

#"using the "color(blue)"trigonometric identity"#

#•color(white)(x)cos(x+y)=cosxcosy-sinxsiny#

#cos45cos120-sin45sin120" is the expansion of"#

#cos(45+120)=cos165^@#

Aug 11, 2018

Please see below.

Explanation:

The question is not clear.So the answer is given for angle #165^circ#

We know that ,

#color(red)(cosalphacosbeta-sinalphasinbeta=cos(alpha+beta)#

Substitute , # alpha=45^circ and beta=120^circ#

#cos45^circcos120^circ-sin45^circsin120^circ#=#cos(45^circ+120^circ)#=#cos165^circ#

#:.cos165^circ=cos45^circ cos120^circ-sin45^circsin120^circ#

Similarly , #color(red)( sin(alpha+beta)=sinalphacosbeta+cosalphasinbeta#

#sin165^circ#=#sin(45^circ+120^circ)#=#sin45^circ cos120^circ+cos45^circsin120^circ#

Now , #color(red)(tan(alpha+beta)=(tanalpha+tanbeta)/(1- tanalphatanbeta)#

#tan165^circ=tan(45^circ+120^circ)=(tan45^circ+tan120^circ)/(1-tan45^circtan120^circ)#