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

[kenshaw93]

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.

 

[tiny-tim]

Welcome to PF!

Hi kenshaw93! Welcome to PF!

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

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.