Video: Simplifying Trigonometric Expressions Using Double-Angle Identities

Write an expression equivalent to cosΒ² (πœ‹/4) βˆ’ sinΒ² (πœ‹/4).

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Video Transcript

Write an expression equivalent to cos squared πœ‹-fourths minus sin squared πœ‹-fourths.

There is a trig identity that states cos squared πœƒ minus sin squared πœƒ is equal to cos of two πœƒ. And looking at our expression, πœ‹ over four can replace πœƒ, which would mean we would know what this is equal to because we can replace πœƒ with πœ‹ divided by four. And this can simplify. The two can go into the four two times.

So we get the cos of πœ‹ over two.

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