Question

If sinx + cosecx = 2, then the value of sin^2016x + cosec^2016x, is -

Answer 1

hope this helps any doubt please comment

Answer 2

Answer:

Hello Ayush4547 ,

Here is your answer !!

sin A + cosec A = 2

=> sin A + 1 / sin A = 2

=> ( sin²A + 1 ) / sin A = 2

=> sin²A + 1 = 2 sin A

=> sin²A - 2 sin A + 1 = 0

=> ( sin A - 1 )² = 0

=> sin A - 1 = 0

=> sin A = 1 ........... ( i )

Since , sin A = 1 ,

cosec A = 1 / sin A = 1 / 1 = 1 .......... ( ii )

From eq. ( i ) and ( ii ) , we get ,

sin^[2016]A + cosec^[2016]A

= ( 1 )^2016 + ( 1 )^2016

= 1 + 1

= 2

So , correct answer is option (3) 2 . [Ans]

Hope it helps you !! :)