SATHEE: Trigonometrical Ratios and Identities 1 Question 9

Trigonometrical Ratios and Identities 1 Question 9

9. The number of ordered pairs $(α, β)$ , where $α, β \in (- π, π)$ satisfying $\cos (α - β) = 1$ and $\cos (α + β) = \frac{1}{e}$ is

(2005, 1M)

(a) 0

(b) 1

(d) 4

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Answer:

Correct Answer: 9. (b)

Solution:

Since, $\cos (α - β) = 1$

$\begin{array}{lrr} \Rightarrow & α - β = 2 n π & But & - 2 π < α - β < 2 π & [as α, β \in (- π, π)] ∴ & α - β = 0 & …(i) Given, & \cos (α + β) = \frac{1}{e} \end{array}$

$\Rightarrow \cos 2 α = \frac{1}{e} < 1$ , which is true for four values of $α$ .

[as $- 2 π < 2 α < 2 π]$

Trigonometrical Ratios and Identities 1 Question 9

9. The number of ordered pairs $(α, β)$ , where $α, β \in (- π, π)$ satisfying $\cos (α - β) = 1$ and $\cos (α + β) = \frac{1}{e}$ is

Answer:

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Trigonometrical Ratios and Identities 1 Question 9

9. The number of ordered pairs (α,β), where α,β∈(−π,π) satisfying cos⁡(α−β)=1 and cos⁡(α+β)=1e is

Answer:

Engineering Preparation

Medical Preparation

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Syllabus

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NCERT Exercise Video Solution

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9. The number of ordered pairs $(α, β)$ , where $α, β \in (- π, π)$ satisfying $\cos (α - β) = 1$ and $\cos (α + β) = \frac{1}{e}$ is