Question

If Cot theta =√9-x^2 find sec theta. tan theta​

Answer 1

Answer:

The answer is $\frac{\sqrt{10-x^2}}{9-x^2}$

Step-by-step explanation:

Given $\cot \theta=\sqrt{9-x^2}$

So $\tan \theta=\frac{1}{\cot \theta}=\frac{1}{\sqrt{9-x^2}}$

Now using, $\sec^2\theta-\tan^2\theta=1$

$\Rightarrow \sec^2\theta-\frac{1}{9-x^2}=1\\\Rightarrow \sec^2\theta=1+\frac{1}{9-x^2}=\frac{9-x^2+1}{9-x^2}=\frac{10-x^2}{9-x^2}\\\\\therefore \sec\theta=\frac{\sqrt{10-x^2}}{\sqrt{9-x^2}}$

Thus

$\sec \theta\cdot \tan\theta=\frac{\sqrt{10-x^2}}{\sqrt9-x^2}\cdot \frac{1}{\sqrt{9-x^2}}=\frac{\sqrt{10-x^2}}{9-x^2}$