Answer:
[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]
sinø=4/5
so
And
cosx=-5/13
so
cos(ø-x)
