Question

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

Answer 1

`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^@`

Answer 2

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)`