How do you simplify # 1 / (1 + cost - i*sint) #?

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Answer 1 · 2018-05-31T02:30:20

#color(crimson)(=> (1/2) * (1 +( i sin t) / (1 + cos t))#

#1 / (1 + cos t - i sin t)#

Multiply and divide by #(1 + cos t - i sin t)#

#=> (1 + cosy + i sin t) / ((1 + cos t - i sin t)(1 + cos t + i sin t))#

#=> (1 + cos t + i sin t) / ((1 + cos t)^2 + sin^2t)#

#=> (1 + cos t + i sin t) / (1 + 2 cos t + cos^2 t + sin^2 t)#

#=> (1 + cos t + i sin t) / (2 + 2 cos t)#

#=> cancel(1 + cos t) / (2 * cancel(1 + cos t) ) + (i sin t) / ((2 * (1 + cos t))#

#color(crimson)(=> (1/2) * (1 +( i sin t) / (1 + cos t))#