Question

please solve this...​

Answer 1

Answer:

Option(B)

Step-by-step explanation:

$Given: tan\ \alpha = \frac{1}{5}$

$\Longrightarrow sin \ \alpha = \frac{1}{\sqrt{26}}$

$\Longrightarrow cos \ \alpha = \frac{5}{\sqrt{26}}$

Now,

$Given: (cosec4\beta - 5sec4\beta)$

$= (\frac{1}{sin4\beta} - \frac{5}{cos4\beta })$

$= \frac{cos4\beta - 5sin4\beta}{sin4\beta cos4\beta}$

$= \frac{2(cos4\beta - 5sin4\beta)}{2sin4\beta cos4\beta}$

$= \frac{2(cos4\beta - 5sin4\beta)}{sin8\beta}$

$= (\frac{2}{sin8\beta}) \ \sqrt{26} (\frac{1}{\sqrt{26}} cos4\beta - \frac{5}{\sqrt{26}} sin4\beta)$

$=(\frac{2\sqrt{26}}{sin8\beta}) (sin\alpha \ cos4\beta - cos\alpha \ sin4\beta)$

$= (\frac{2\sqrt{26} }{sin8\beta})(sin(\alpha-4\beta))$

$= (\frac{2\sqrt{26} } {sin8\beta})(sin(12\beta - 4\beta))$

$=(\frac{2\sqrt{26} } {sin8\beta})(sin8\beta)$

$= 2\sqrt{26}$

$= \boxed{\sqrt{104}}$

Hope it helps!

Answer 2

hope it helps!!.............