How do you write the expression as the sine, cosine, or tangent of the angle given ${cos 45}^{\circ} {cos 120}^{\circ} - {sin 45}^{\circ} {sin 120}^{\circ}$ $cos45^circcos120^circ-sin45^circsin120^circ$ ?

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How do you write the expression as the sine, cosine, or tangent of the angle given ${cos 45}^{\circ} {cos 120}^{\circ} - {sin 45}^{\circ} {sin 120}^{\circ}$ $cos45^circcos120^circ-sin45^circsin120^circ$ ?

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Answer 1 · 2018-08-11T09:42:26

${cos 165}^{\circ}$ $cos165^@$

Explanation:

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

$∙ x cos (x + y) = cos x cos y - sin x sin y$ $•color(white)(x)cos(x+y)=cosxcosy-sinxsiny$

$cos 45 cos 120 - sin 45 sin 120 is the expansion of$ $cos45cos120-sin45sin120" is the expansion of"$

$cos (45 + 120) = {cos 165}^{\circ}$ $cos(45+120)=cos165^@$

Answer 2 · 2018-08-11T09:49:59

Please see below.

Explanation:

The question is not clear.So the answer is given for angle $165^{\circ}$ $165^circ$

We know that ,

$cos α cos β - sin α sin β = cos (α + β)$ $color(red)(cosalphacosbeta-sinalphasinbeta=cos(alpha+beta)$

Substitute , $α = 45^{\circ} and β = 120^{\circ}$ $alpha=45^circ and beta=120^circ$

${cos 45}^{\circ} {cos 120}^{\circ} - {sin 45}^{\circ} {sin 120}^{\circ}$ $cos45^circcos120^circ-sin45^circsin120^circ$ = $cos (45^{\circ} + 120^{\circ})$ $cos(45^circ+120^circ)$ = ${cos 165}^{\circ}$ $cos165^circ$

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

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

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

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

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

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How do you write the expression as the sine, cosine, or tangent of the angle given ${cos 45}^{\circ} {cos 120}^{\circ} - {sin 45}^{\circ} {sin 120}^{\circ}$ $cos45^circcos120^circ-sin45^circsin120^circ$ ?

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Explanation:

Explanation:

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Explanation:

Explanation:

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How do you write the expression as the sine, cosine, or tangent of the angle given ${cos 45}^{\circ} {cos 120}^{\circ} - {sin 45}^{\circ} {sin 120}^{\circ}$ $cos45^circcos120^circ-sin45^circsin120^circ$ ?