Question

Sin theta + cosec theta =2. Prove that sin n theta + cosec n theta =2

Answer 1

Answer:

Sin A + Cosec A = 2

=> Sin A + ( 1 / Sin A ) = 2

Taking LCM we get,

=> ( Sin² A + 1 ) / Sin A = 2

=> Sin²A + 1 = 2 SinA

=> Sin²A - 2 SinA + 1 = 0

=> Sin A ( Sin A - 1 ) - 1 ( Sin A - 1 ) = 0

=> ( Sin A - 1 ) ( Sin A - 1 ) = 0

=> ( Sin A - 1 )² = 0

Taking Square root on both sides we get,

=> Sin A - 1 = 0

=> Sin A = 1

=> Cosec A = 1 / Sin A

=> 1 / 1 = 1

Hence,

Sinⁿ A + Cosecⁿ A = 1ⁿ + 1ⁿ = 1 + 1 = 2

Hence Proved !