IIT JEE , AIEEE Forum - Mathematics , Trignometry

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express in terms of x + iy

____________1______________
1- cos theta + 2i sin theta

Greatdreams

1 / 1 - cos x + 2 i sin x

= 1/ (2 sin ² x/2 + 4 i sin x/2 cos x/2 )

= 1/ (2 sin x/2 ) . 1/( sin x/2 + 2 i cos x/2 )

= 1/ (2 sin x/2 ) . (sin x/2 - 2i cos x/2) / ( sin ²x/2 + 4 cos² x/2 )

= ( 1 - 2 i cot x/2 ) / ( 2 sin ² x/2 + 8 cos ² x/2)

= ( 1 - 2i cot x/2 ) / ( 5 + 3 cos x )

hsbhatt

$= rac{1}{2sin^2 rac{ heta}{2} + i2 sin rac{ heta}{2} cos rac{ heta}{2}}$

= rac{1}{2sin rac{ heta}{2}} rac{1} {left( sin rac{ heta}{2} + icos rac{ heta}{2} ight)}

= rac{1}{2sin rac{ heta}{2}} left( sin rac{ heta}{2} - icos rac{ heta}{2} ight)

= rac{1}{2} - rac{i}{2} cot rac{ heta}{2}

Sorry, I seem to have solved another prob!

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