Question

Sin a+cosec a=2,prove that sin6a+cosec6a=2

Answer 1

Answer:

Given Equation is Sina + coseca = 2.

On cubing both sides, we get

(Sina + coseca)^3 = (2)^3

sin^3a + cosec^3a + 3 * sina * coseca(Sin a + coseca) = 8

sin^3a + cosec^3a + 3 * sina * 1/sina(sina + coseca) = 8

sin^3a + cosec^3a + 3 * 1(2) = 8

sin^3a + cosec^3a + 6 = 8

sin^3a + cosec^3a = 8 - 6

sin^3a + cosec^3a = 2.

Hope this helps. Happy learning!!!