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Given: sin = 4/5 and cos x = -5/13 ; evaluate the following expression.

cos( ∅ - x )
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sinø=4/5

so

- cosø=3/5

And

cosx=-5/13

so

- sinx=12/13

cos(ø-x)

- sinøsinx+cosøcosx
- (4/5)(12/13)+(3/5)(-5/13)
- (48/65)-(15/65)
- 48-15/65
- 33/65
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[tex]\cos(\theta - x)=\dfrac{33}{65}[/tex]

Step-by-step explanation:

Given:

[tex]\sin\theta=\dfrac{4}{5}\implies \cos \theta=\dfrac{3}{5}[/tex]

[tex]\cos x=-\dfrac{5}{13}\implies \sin x=\dfrac{12}{13}[/tex]

Using the trig identity:

[tex]\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B[/tex]

[tex]\begin{aligned}\implies \cos(\theta - x) &=\cos \theta \cos x + \sin \theta \sin x\\\\&=\dfrac{3}{5} \cdot -\dfrac{5}{13} + \dfrac{4}{5} \cdot \dfrac{12}{13}\\\\&=-\dfrac{15}{65} + \dfrac{48}{65}\\\\&=\dfrac{33}{65}\end{aligned}[/tex]
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