Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 8 - Section 8.1 - Complex Numbers - 8.1 Problem Set - Page 426: 33

Answer

x=$\frac{\pi}{2}$ and y=$\frac{\pi}{4}$ or y=$\frac{5 \pi}{4}$

Work Step by Step

So, (Sin^{2} x+1 ) + i tan y = 2sin x+i Now By comparing the like terms on both sides, we will get $Sin^{2} x +1 = 2 sin x, tan y=1$ => $Sin^{2} x - 2 Sin x +1 = 0, tan y =1$ =>$( sin x - 1)^{y}=0 , tan y =1$ => sin x =1, tan y=1 => x=$\frac{\pi}{2}$ and y=$\frac{\pi}{4} $or $ y=\frac{5 \pi}{4}$
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