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 cos² (𝜋/4) − sin² (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 𝜃 is equal to cos squared 𝜃 minus sin squared 𝜃. The expression in this question is written in the same form as the right-hand side of the identity, where 𝜃 is equal to 𝜋 over four. This means that two 𝜃 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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