Question

If cot = 1/root3 then find value of 1-cos^2/1+cos^2

Answer 1

Answer:

Given cot\theta = \frac{1}{\sqrt{3}}

\implies cot\theta = cot60

\implies \theta = 60---(1)

Now ,

LHS = \frac{1-cos^{2}\theta}{2-sin^{2}\theta}

= \frac{1-cos^{2}60}{2-sin^{2}60}

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

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

= \frac{\frac{(4-1)}{4}}{\frac{(8-3)}{4}}

=\frac{\frac{3}{4}}{\frac{5}{4}}

After cancellation, we get

= \frac{3}{5}

Step-by-step explanation:Hope this is helpful for you