Question Video: Simplifying Trigonometric Expressions Using Double-Angle Identities | Nagwa Question Video: Simplifying Trigonometric Expressions Using Double-Angle Identities | Nagwa

# Question Video: Simplifying Trigonometric Expressions Using Double-Angle Identities Mathematics • Second Year of Secondary School

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Which of the following expressions is equivalent to cosΒ² (π/4) β sinΒ² (π/4)? [A] cos (π/4) [B] 2 cos (π/4) [C] cos (π/2) [D] sin (π/2) [E] 2 sin (π/4)

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### Video Transcript

Which of the following expressions is equivalent to cos squared π over four minus sin squared π over four? (A) cos π over four, (B) two cos π over four, (C) cos π over two, (D) sin π over two, or (E) two sin π over four.

In order to answer this question, we begin by recalling one of the double-angle identities. cos two π is equal to cos squared π minus sin squared π. The expression in this question is written in the same form as the right-hand side of the identity, where π is equal to π over four. This means that two π is equal to two multiplied by π over four, which is equal to π over two.

We can therefore conclude that cos squared π over four minus sin squared π over four is equal to cos π over two. And the correct answer is option (C).

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