Answer:
Value of the expression = 16
Step-by-step explanation:
Given expression is,
[Sin²θ - (Cosθ)(Sinθ)]⁻¹
By substituting θ = 30° in the expression,
[Sin²(30)° - (Cos²30°)(Sin²30°)]
= [(Sin30°)² - (Cos30)²(Sin²30)]
= [tex][(\frac{1}{2})^{2}-(\frac{\sqrt{3}}{2})^2(\frac{1}{2})^2]^{-1}[/tex]
= [tex][\frac{1}{4}-(\frac{3}{4})(\frac{1}{4})]^{-1}[/tex]
= [tex][\frac{1}{4}-\frac{3}{16}]^{-1}[/tex]
= [tex](\frac{1}{16})^{-1}[/tex]
= 16
