How to Calculate Sin(π/8)^2 - Cos(3π/8)^4 Without a Calculator?

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kenshaw93
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Homework Statement


Without using tables(calculators) find the numerical value of

Sin[Pi/8]^2 - Cos[3 (Pi/8)]^4



Homework Equations






The Attempt at a Solution


I tried changing it to:
1-cos[pi/8]^2 - cos[3pi/8]^4 but have no idea where to go... its really got me scratching my head.

Any ideas? Any help is much appreciated, thank you.
 
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Welcome to PF!

Hi kenshaw93! Welcome to PF! :smile:

(have a pi: π and try using the X2 tag just above the Reply box :wink:)

You know what cos and sin of π/4 are …

so use one of the standard trigonometric identities to get to π/8 and 3π/8. :smile: