Question

please answer fastly. tomorrow for me exam

Answer 1

hey mate.
here's the solution

Answer 2

Answer:

$\boxed{2x}}$

Step-by-step explanation:

We know that:

$cot^2\theta = cosec^2\theta - 1$

$\implies cot^2\theta = ( x + \frac{1}{4x})^2 - 1$

$\implies cot^2\theta = x^2 + \frac{1}{16 x^2} + 2\times x\times \frac{1}{4x} - 1$

$\implies cot^2 \theta = x^2 + \frac{1}{16x^2} - \frac{1}{2}$

$\implies cot^2 \theta = ( x - \frac{1}{4x} ) ^2$

$\implies cot \theta = x - \frac{1}{4x}$

$cot\theta + cosec\theta$

$\implies x + \frac{1}{4x} + x - \frac{1}{4x}$

$\implies 2x$

Hope it helps you

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