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State whether the following equation has a solution or not? cos 2θ = 13 - Mathematics and Statistics

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Question

State whether the following equation has a solution or not?

cos 2θ = `1/3`

Sum
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Solution

Given:

cos 2θ = `1/3`

This value, `1/3` lies between −1 and 1, and the cosine function can take any value in that range.

−1 ≤ `1/3` ≤ 1

So the equation: cos 2θ = `1/3`

has real solutions

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Chapter 3: Trigonometric Functions - Miscellaneous exercise 3 [Page 109]

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Balbharati Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 3.1 | Page 109

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