Question

if sin theta + cosec theta equal to 2 then find the value of sin 2016 theta + cosec 2016 theta

Answer 1

sin theta + cosec theta =2

or, sin theta+1/sin theta=2

or, (sin^2theta+1)/sin theta=2

or, sin^2theta +1=2sin theta

or, sin^2theta -2sin theta+1=0

or, (sin theta)^2 - 2×sin theta×1 +1^2=0

or, (sin theta - 1)^2=0

or, sin theta - 1 =0

or, sin theta = 1

so cosec theta

=1/sin theta

=1/1

=1

hence,

sin^2016 theta + cosec^2016 theta

= (sin theta)^2016+(1/sin theta)^2016

= 1^2016 + 1^2016

=1 + 1

=2(answer)

hope this helps...please mark this brainliest •••