Question

I need answers with steps pleaseeeer

Answer 1

Method1:

Let sinΘ be x ⇒ cosecΘ = 1/x

So x+1/x = 2

cubing on both sides

⇒ (x+1/x)³ = 2³

⇒x³ + 1/x³ + 3*x*1/x * (x+1/x) = 8

⇒ x³ + 1/x³ + 3*(2) = 8

⇒ x³ + 1/x³ = 8-6 = 2

squaring on both sides

⇒  { x³ + 1/x³ }² = 2²

⇒ x⁵ + 1/x⁵ + 2*x³*1/x³ = 4

⇒  x⁵ + 1/x⁵ + 2 =4

⇒ x⁵ + 1/x⁵ = 2

So sin⁵Θ + cosec⁵Θ = 2

Method 2 ;

For objective type we can easily guess x+1/x = 2 ⇒ x = 1

So x⁵ + 1/x⁵ = 2