Question

prove the






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Answer 1

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1 answer · Mathematics
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Do you know this identity:

sin(a - b) = sin(a).cos(b) - cos(a).sin(b)

sin(30 - 11) = sin(30).cos(11) - cos(30).sin(11)

sin(19) = (1/2).cos(11) - [(√3)/2].sin(11)

sin(19) + cos(11) = (1/2).cos(11) - [(√3)/2].sin(11) + cos(11)

sin(19) + cos(11) = (3/2).cos(11) - [(√3)/2].sin(11)

sin(19) + cos(11) = (1/2).[3.cos(11) - √3.sin(11)] ← memorise this result as (1)


Do you know this identity:

cos(a - b) = cos(a).cos(b) + sin(a).sin(b)

cos(30 - 11) = cos(30).cos(11) + sin(30).sin(11)

cos(19) = [(√3)/2].cos(11) + (1/2).sin(11)

cos(19) - sin(11) = [(√3)/2].cos(11) + (1/2).sin(11) - sin(11)

cos(19) - sin(11) = [(√3)/2].cos(11) - (1/2).sin(11)

cos(19) - sin(11) = (1/2).[√3.cos(11) - sin(11)] ← memorise this result as (2)


= [sin(19) + cos(11)] / [cos(19) - sin(11)] → recall (1)

= { (1/2).[3.cos(11) - √3.sin(11)] } / [cos(19) - sin(11)] → recall (2)

= { (1/2).[3.cos(11) - √3.sin(11)] } / { (1/2).[√3.cos(11) - sin(11)] } → you can simplify by (1/2)

= [3.cos(11) - √3.sin(11)] / [√3.cos(11) - sin(11)] → you factorize (√3) at the numerator

= (√3).[√3.cos(11) - sin(11)] / [√3.cos(11) - sin(11)] → you simplify

= √3
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