Question

Question 9
If $\sqrt{3}tan\theta =1$, find the value of $si{n}^2\theta -co{s}^2\theta$.

Answer 1

Given that, $\sqrt{3}tan\theta =1$

$\Rightarrow tan\theta =\frac{1}{\sqrt{3}}=tan{30}^{\circ }$

$\Rightarrow \theta ={30}^{\circ }$

Now, $si{n}^2\theta -co{s}^2\theta =si{n}^2{30}^{\circ }-co{s}^2{30}^{\circ }$

$={\left(\frac{1}{2}\right)}^2-{\left(\frac{\sqrt{3}}{2}\right)}^2$

$=\frac{1}{4}-\frac{3}{4}=\frac{1-3}{4}=-\frac{2}{4}=-\frac{1}{2}$