Question

if sina+cosec=2 THEN FIND sin^2016A +cosec^2016A

Answer 1

Hey!!!!!

We have

sinA + cosecA = 2

=>sinA + 1/sinA = 2

=> sin²A + 1 = 2sinA

=> sin²A + 1 - 2sinA = 0

=> (sinA - 1)² = 0

=> sinA = 1

Thus A = 90°

Thus sin^2016 A + cosec^2016 A = 1 + 1
=> 2

Hope this helps you

Answer 2

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♦♦ ( sin A + cosec A ) = 2

=> ( sin² A + 1 ) = 2 sin A

=> ( sin² A - 2sin A + 1 ) = 0
=> ( sin A - 1 )² = 0

=> ( sin A ) = 1
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=> ( sin²⁰¹⁶ A + cosec²⁰¹⁶ A ) = ( 1 + 1 ) = 2

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Cheers ♥ Amon