Question

​​ If sin θ + cosec θ = 2, then find then find the value of sin 8 θ + cosec 8 θ.

Answer 1

sinA + cosecA = 2
sin^2A + 1 = 2 sinA
sin^2A -2 sinA +1=0
(sinA -1 )^2 =0
sinA -1 = 0
sinA = 1
A = pi/2
now
sin8A + cosec8A
= sin8pi/2 + cosec8pi/2
=sin4pi + cosec4pi
= 0

Answer 2

Ans is 2. If sin + cosec=2 then sin6+cosec6=2