Question

if cosecA - cotA = 1/4, then find the value of cosecA + cotA.

Answer 1

Given that cosec A - cot A = 1/4.

We know that cosec^2 A - cot^2 A = 1

We know that a^2 - b^2 = (a - b)(a + b)

                        (cosecA - cotA)(cosecA + cotA) = 1

                        (1/4)(cosecA+cotA) = 1

                         cosecA + cotA = 4.


Hope this helps!

Answer 2

Answer:

The answer is 4.

Step-by-step explanation:

Since, we know the trigonometric identity,

cosec² x - cot² x = 1

Similarly,

cosec² A - cot² A = 1

⇒ ( cosec A + cot A ) (cosec A - cot A) = 1  ( Since, a² - b² = (a+b)(a-b) )

We have given,

$cosec x - cot x = \frac{1}{4}$,

$( cosec x + cot x ) \times \frac{1}{4} = 1$

$\implies cosec A + cot A ) = 4$