Question

if cot theta= 1/ root 3, show that 1-cos square theta/ 2- sin square theta = 3/5.

Answer 1

Hey mate here is your answer

Hope it will help you

Answer 2

Solution:

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

= $\frac{3}{5}$

= RHS

•••••