Question

if sin A=3/4 calculate cosec A and cot A​

Answer 1

Answer:

$\cosec(a) = \frac{4}{3}$

$\cot(a) = \frac{ \sqrt{7} }{3}$

Step-by-step explanation:

Given:

sin a = 3/4

To find:

cosec a and cot a

Proof:

We know that,

$\sin(a) = \frac{1}{ \cosec(a) }$

On substituting sin a value in the above expression, we have,

$\frac{3}{4} = \frac{1}{cosec(a)}$

$cosec(a) = \frac{1}{ \frac{3}{4} }$

$cosec(a) = \frac{4}{3}$

We know that,

${cosec}^{2} (a) - { \cot }^{2} (a) = 1$

${ \cot }^{2} (a) = {cosec}^{2} (a) - 1$

On substituting cosec a value on the above expression, we have,

${cot}^{2} (a) = {( \frac{4}{3}) }^{2} - 1$

${cot}^{2}( a )= \frac{16}{9} - 1$

${cot}^{2}( a) = \frac{16 - 9}{9}$

${cot}^{2} (a )= \frac{7}{9}$

$\cot(a) = \sqrt{ \frac{7}{9} }$

$\cot(a) = \frac{ \sqrt{7} }{3}$

Therefore, cosec(a) is 4/3 and cot(a) is root7/3.

Hope it helps you.

Good Luck.