Question

Please help guys!
If sin A + cosec A = 2, then the value of
sin^[2016]A + cosec^[2016]A, is -
(1) 1 (2) 2016 (3) 2 (4) 4032

Answer 1

hey dear

here is your answer

Solution

Given

SinA + CosecA =2

squaring on both the sides

( SinA + CosecA) ^2A = 2^2

Sin^2A + Cosec^2A + 2 SinA cosec = 4

Sin^A + Cosec^2A = 4 - 2 Sina CosecA

CosecA = 1/SinA

so

Sin^2A + Cosec^2A = 4 - 2

Sin^2A + Cosec^2A = 2

it is the answer

hope it helps

thank you

Answer 2

Hello Codeist ,
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 !! :)