Question

Cosecx-cotx is equal to 1/4 then cosecx+cotx

Answer 1

Answer:

according to question :-

cosec x - cot x = 1/4

1/sin x - 1/tan x = 1/4

1/sin x - cos x / sin x = 1/4

1-cos x / sin x = 1/4

cos x / sin x = 1/4+1

cos x / sin x = 5/4

cos x = 5

sin x = 4

hope you understand plz thank my answer

Answer 2

The value of $\csc x+\cot x$ is 'equal to 4'.

Step-by-step explanation:

We have,

$\csc x-\cot x=\dfrac{1}{4}$                       ...... (1)

To find, the value of $\csc x+\cot x$ = ?

We know that, the trigonometric identity

$\csc^2 A-\cot^2 A$ = 1

Using algebraic identity,

$a^{2}-b^{2} =(a+b)(a-b)$

$(\csc x+\cot x)(\csc x-\cot x)=1$

⇒ $(\csc x+\cot x)(\csc x-\cot x)=1$

From equation (1), we get

⇒ $(\csc x+\cot x)(\dfrac{1}{4} )=1$

⇒ $\csc x+\cot x$ = 4

∴ The value of $\csc x+\cot x$ = 4

Thus, the value of $\csc x+\cot x$ is equal to 4.