Question

If tan theta +cot theta=4,find value of tan4theta+cot4theta.

Answer 1

Answer:

$\text{The value of }\bf\,tan\,4\theta+cot\,4\theta\text{ is }\frac{4}{\sqrt3}}$

Step-by-step explanation:

$\text{Given:}$

$tan\theta+cot\theta=4$

$\implies\frac{sin\theta}{cos\theta}+\frac{cos\theta}{sin\theta}=4$

$\implies\frac{sin^2\theta+cos^2\theta}{sin\theta\,cos\theta}=4$

$\implies\frac{1}{sin\theta\,cos\theta}=4$

$\implies\frac{1}{4}=sin\theta\,cos\theta$

$\implies\frac{1}{2}=2\,sin\theta\,cos\theta$

$\implies\,sin\,2\theta=\frac{1}{2}$

$\implies\,2\theta=30^{\circ}$

$\implies\theta=15^{\circ}$

$\text{Now,}$

$tan\,4\theta+cot\,4\theta$

$=tan\,4(15^{\circ})+cot\,4(15^{\circ})$

$=tan\,60^{\circ}+cot\,60^{\circ}$

$=\sqrt{3}+\frac{1}{\sqrt3}$

$=\frac{3+1}{\sqrt3}$

$=\frac{4}{\sqrt3}$

$\implies\boxed{\bf\,tan\,4\theta+cot\,4\theta=\frac{4}{\sqrt3}}$

Answer 2

Answer:

194

Step-by-step explanation: