Question

✴️CONTENT QUALITY ANSWER✴️

PROVE :
$cosec^6 a - cot^{6} a = 1 + 3cot ^{2}a \times cosec^{2}a$
❌ IDIOTIC answers ❌ will be immediately reported ...

Answer 1

Given LHS = (cosec^6a), It can be written as:

(cosec^6a) = (cosec^2a)^3

                   = (cot^2a + 1)^3

We know that (x + y)^3 = x^3 + y^3 + 3xy(x + y)

 cosec^6a = (cot^2a)^3 + 1^3 + 3(cot^2a)(1)(cot^2a + 1)

cosec^6a = (cot^2a)^3 + 1 + 3cot^2a(cosec^2a)

cosec^6a = cot^6a + 1 + 3cot^2a * cosec^2a

cosec^6a - cot^6a = 1 + 3cot^2a * cosec^2a.


LHS = RHS


Hope this helps!