Question

use double angle formula to find the exact value of 2cos^2(3pie/8)-1

Answer 1

Okay...

Answer 2

Use the fact that\[\cos{2 \theta}=\cos^2 \theta -\sin^2 \theta=2\cos^2 \theta -1\]

Answer 3

For\[\theta = \frac{3\pi}{8}\]\[\cos 2 \theta =\cos \frac{3 \pi}{4}=\cos^2 \frac{3 \pi}{8}-1\]The right-hand side is your expression. Now

Answer 4

\[\frac{3\pi}{4}\] lies in the second quadrant where cosine is negative. 3pi/4 is equivalent to 135 degrees. The cosine of 135 degrees is equal to the the negative cosine of 45 degrees, which has an exact value of \[-\frac{1}{\sqrt{2}}\]

Answer 5

thank you!!!

Answer 6

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Answer 7

what is the exact value of 2sin 157.5 cos 157.5

Answer 8

This is an example of double angle for sine.\[\sin 2 \theta = 2 \sin \theta \cos \theta\]Here theta is 157.5, so 2 x theta = 315 degrees.

315 = 360 - 45

This lies in the fourth quadrant where sine is negative.

You have sin(315)=-sin(45)= -1/sqrt(2) again.

Answer 9

it says write the following expression as sin cos or tan of a double agent. then find the exact value