Question

Yusuf used the equation cos⁡ 80°=2 cos² 40°−1 to find cos⁡ 80°. Which trigonometric identity did Yusuf use?

sum identity for cosine

double-angle identity for cosine difference

identity for cosine

half-angle identity for cosine

Answer 1

Yusuf used the double-angle identity for cosine difference ⇒ 2nd answer

Step-by-step explanation:

Let us revise the identities of double an angle

• sin(2x) = 2 sin(x) cos(x)
• cos(2x) = cos²(x) - sin²(x)
• cos(2x) = 2 cos²(x) - 1
• cos(2x) = 1 - 2 sin²(x)

∵ Yusuf used the equation cos(80)° = 2 cos²(40)° - 1

∵ 80 = 2 × 40

∴ 80 is the double of 40

∵ cos(2x) = 2 cos²(x) - 1

∴ 2x = 80° and x = 40°

∴ The identity is double-angle identity for cosine difference

Yusuf used the double-angle identity for cosine difference

Learn more:

You can learn more about the trigonometry identities in brainly.com/question/2285189

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