opium46 opium46
  • 02-06-2021
  • Mathematics
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Use a half-angle identity to find the exact value of cos 15º.

Use a halfangle identity to find the exact value of cos 15º class=

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Luv2Teach
Luv2Teach Luv2Teach
  • 04-06-2021

Answer:

Step-by-step explanation:

[tex]cos15=cos\frac{30}{2}[/tex] so the angle we will use in our identity is 30 degrees. The formula is

[tex]cos\frac{30}{2}=\sqrt{\frac{1+cos30}{2} }[/tex] which simplifies to

[tex]\sqrt{\frac{1+\frac{\sqrt{3} }{2} }{2} }[/tex] which simplifies to

[tex]\sqrt{\frac{\frac{2+\sqrt{3} }{2} }{2} }[/tex] which simplifies to

[tex]\sqrt{\frac{2+\sqrt{3} }{4} }[/tex] which simplifies, finally, to

[tex]\frac{\sqrt{2+\sqrt{3} } }{2}[/tex], choice a.

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