Question

If tan theta= 3/4 , find csc theta

Answer 1

Answer:

$csc\theta=\frac{5}{3}$

Step-by-step explanation:

Given:

$tan\theta =\frac{3}{4}$

$cot\theta =\frac{4}{3}$                 [∵ $cot\theta =\frac{1}{tan\theta}$ ]

Squaring both sides.

$cot^2\theta =\frac{4^2}{3^2}=\frac{16}{9}$

$csc^2\theta -1=\frac{16}{9}$        [∵ $cot^2\theta =csc^2\theta-1]$ ]

Adding 1 to both sides.

$csc^2\theta -1+1=\frac{16}{9}+1$

$csc^2\theta =\frac{16}{9}+1$

$csc^2\theta=\frac{16}{9} +\frac{9}{9}$     [Taking LCD=9 and adding fractions ]

$csc^2\theta=\frac{16+9}{9}$

$csc^2\theta=\frac{25}{9}$

Taking square root both sides.

$\sqrt{csc^2\theta}=\sqrt{\frac{25}{9}}$

∴ $csc\theta=\frac{5}{3}$