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2cos² 34° - 1 expressed as a single trigonometric ratio? (With explanation of steps please)

User Kyshia
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1 Answer

5 votes

Answer:

Cos 68

Explanation:

Given the expression 2cos² 34° - 1, we are to expression as a single trig ratio.

Let the angle be theta

Recall that sin²theta + cos²theta = 1

sin²theta = 1 - cos²theta ... 1

also Cos 2theta = Cos²theta - sin²theta ... 2

Substitute 1 into 2

Cos 2theta = Cos²theta - (1-cos²theta)

Cos 2theta = Cos²theta - 1 + cos²theta

Cos 2theta = 2Cos²theta - 1

Replace theta with 34

Cos 2(34)= 2Cos²(34)- 1

Cos 68 = 2Cos²(34)- 1

Hence the single trig expression is Cos 68

User Hearty
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