Question

If 4x=cosec theta and 4/x=cot theta, then find the vlue of 4(x2-1/x2)

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

Answer 2

Answer is 1/4

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