Question

If 4x=cosec theta and 8/x=cot theta ,then find the value of 4(x square -1/x square)

Answer 1

Answer:

1/4

Step-by-step explanation:

Given 4x=cosec theta and 8/x=cot theta,

there is a mistake 4/x=cot theta,

Now consider , 4(x² - 1/x²)

=4(x-1/x)(x+1/x)

We have x = cosec∅/4

1/x = cot∅/4

=> (x + 1/x) = 1/4(cosec∅ + cot∅)

=>(x - 1/x) = 1/4 (cosec∅ - cot∅)

=>4(x + 1/x)(x - 1/x)

= 4*1/4((cosec∅ + cot∅)*1/4* (cosec∅ - cot∅)

=1/4(cosec²∅ - cot²∅)

=1/4 (Since cosec²∅ - cot²∅ = 1)

=1/4.----Ans