Question

If sin theta + cosec theta = 2 then sin^n theta + cosec^n theta =

Answer 1

sin∅ +cosec∅ =2

sin∅ + 1/sin∅ =2

sin²∅ +1 = 2sin∅

sin²∅ -2sin∅ +1 =0

(sin∅ -1)² =0

sin∅ = 1

hence ,
cosec∅ = 1

now,
sinⁿ∅ + cosecⁿ∅ = (1)ⁿ + (1)ⁿ =1 + 1 =2

Answer 2

HI DEARS

LET, SIN THETA = X ; AND

WE KNOW THAT COSEC THETA = 1/SIN THETA

SO, LET Y = 1/X

WE USING  THE FORMULA :- (X+Y)²= X²+Y²+2XY

SO,  ==> (X+1/X)² =  X²+1/X²+2×X×1/X

==>  X²+1/X²+2

==> X²+1/X² = -2

I HOPE ITS HELPFUL