Question

Given that cosec A + cot A = 1/4. Then,what is the value of cosec A - cot A?

Answer 1

Answer:

given cosecA + cotA= 1/4

cosecA = 1/4- cotA

thus,

putting value of cosecA

cosecA + cotA=1/4

1/4- cotA- cotA=1/4

1/4-2cotA=1/4

cotA= 0

therefore

cosecA=1/4

cosecA-cotA

1/4-cotA-cotA

= 1/4-0

1/4

Answer 2

Answer:Given that

Cosec A+ cot A=1/4

Using identity

Cosec^2 =cot^2+1

So value of 1= cosec A ^2-cot A^2

Therefore

Cosec a square - cot square a= 1

Using identity

A square- b square =(a+b) (a-b)

So (cosec a - cot a) (cosec a+cot a) =1

(Cosec a- cot a) (1/4) =1

(Cosec a- cot a) =1×4

(Cosec A -cot A) =4

I hope it help you