Since
[tex]\csc(x)=\dfrac{1}{\sin(x)}[/tex]
we have
[tex]\csc(x)\sin(x)+\tan(x) = \dfrac{1}{\sin(x)}\cdot \sin(x)+\tan(x)=1+\tan(x)[/tex]
And since
[tex]\tan(x)=\dfrac{8}{15}[/tex]
we have
[tex]1+\tan(x) = 1-\dfrac{8}{15}=\dfrac{15}{15}-\dfrac{8}{15}=\dfrac{7}{15}[/tex]
The value of cscθ sinθ + tan θ is 7/15.
cscθ is the reciprocal of sinθ.
The expression is given by cscθ sinθ + tan θ.
We can simplify this expression before solving it.
Let the expression be y = cscθ sinθ + tan θ.
cscθ = 1/sinθ
y = sinθ * 1/sinθ + tan θ
y = 1 + tan θ
The value of tan θ is given as -8/15.
We can substitute this above:
y = 1 + tan θ
= 1 - 8/15
= (15-8)/15
= 7/15
The value of the expression cscθ sinθ+ tan θ is found to be 7/15.
Therefore, the value of cscθ sinθ + tan θ is 7/15.
Learn more about trigonometric ratios here: https://brainly.com/question/24349828
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