Question

solve the equation tan^2theta+cot^2theta=2​

Answer 1

Answer:

The answer is $\theta=n\pi\pm \frac{\pi}{4}$

Step-by-step explanation:

Given $\tan^2\theta+\cot^2\theta=2$

         $\Rightarrow \tan^2\theta+\cot^2\theta-2=0\\\Rightarrow \tan^2\theta+\cot^2\theta-2\tan\theta\cot \theta=0$, using identity $\tan\theta\cot \theta=1$

        $\Rightarrow (\tan\theta-\cot \theta)^2=0\\\Rightarrow (\tan\theta-\cot \theta)=0\\\Rightarrow \tan\theta=\cot\theta=\frac{1}{\tan\theta}\\\\\Rightarrow \tan^2\theta=1=\tan^2{\frac{\pi}{4}}$

Thus the general solution is

                      $\theta=n\pi\pm \frac{\pi}{4}$, $n\in Z$

Since general solution of $\tan^2\theta=\tan^2\alpha$ is $\theta=n\pi\pm \alpha$