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If cosx cos(pi/7) + sinx sin(pi/7) = -(sqrt(2))/2, then x can equal...? (Check all that apply) (Will give medal & fan!) A. pi/4 + pi/7 + 2npi B. 5pi/4 + pi/7 + 2npi C. 7pi/4 + pi/7 + 2npi D. 3pi/4 + pi/7 + 2npi

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alondomarksman1
 If sinxcos(π/7) - sin(π/7) cosx = - √ 2 / 2 , then x can equal: ______ Check all that apply: 1)π/4 ... Best Answer: sin ( x - ( pi / 7 ) ) = - sqrt ( 2 ) / 2

Answer:

Options B and D

Step-by-step explanation:

Given that

[tex]cos x cos \frac{\pi}{7} +sinx sin \frac{\pi}{7} =\frac{-\sqrt{2} }{2}[/tex]

Use the formula for sum angles for Cos as

Cos A cos B +sin A sin B = cos (A-B)

we have

[tex]cos (x-\frac{\pi}{7} ) = \frac{-\sqrt{2} }{2}[/tex]

First let us solve principal solution

cos negative in the II quadrant

Hence principal soluton is [tex]\pi-\frac{\pi}{4} =\frac{3\pi}{4}[/tex]+[tex]\frac{\pi}{7}[/tex]

Again it is negative in third quadrant i.e. x = [tex]\frac{5\pi}{4}[/tex]+[tex]\frac{\pi}{7}[/tex]

General solution is [tex]\frac{5\pi}{4}[/tex]+[tex]\frac{\pi}{7}+2n\pi and\\\\\frac{3\pi}{4}[/tex]+[tex]\frac{\pi}{7}+2n\pi[/tex]

Options B and D

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