Question

prove that 2cos²theta+2/1+cos²theta=2 ​

Answer 1

Step-by-step explanation:

$\sf 2cos^2 \theta + \dfrac{2}{1 + cot^2 \theta} = 2$

Now let's consider LHS

$\Rightarrow \sf 2cos^2 \theta + \dfrac{2}{1 + cot^2 \theta} \\\\\\ \Rightarrow \sf 2cos^2 \theta + \dfrac{2}{cosec^2 \theta} \\\\\\ \Rightarrow \sf \dfrac{2cos^2 \theta.cosec^2 \theta + 2 }{ cosec^2 \theta } \\\\\\ \Rightarrow \sf \dfrac{ 2cot^2 \theta + 2 }{ cosec^2 \theta } \\\\\\ \Rightarrow \sf \dfrac{ 2( 1 + cot^2 \theta) }{ cosec^2 theta } \\\\\\ \Rightarrow \sf \dfrac{ 2cosec^2 \theta }{ cosec^2 \theta } = 2 = RHS$

Hence proved.