SATHEE: Trigonometrical Equations 3 Question 2

Trigonometrical Equations 3 Question 2

2. The number of solutions of the pair of equations $2 \sin^{2} θ - \cos 2 θ = 0$ and $2 \cos^{2} θ - 3 \sin θ = 0$ in the interval $[0, 2 π]$ is

(a) 0

(b) 1

(d) 4

(2007, 3M)

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Answer:

Correct Answer: 2. (c)

Solution:

$2 \sin^{2} θ - \cos 2 θ = 0$

$\Rightarrow \sin^{2} θ = \frac{1}{4}$

Also, $2 \cos^{2} θ = 3 \sin θ$

$∴ \sin θ = \frac{1}{2}$

$[∵ \sin θ + 2 \neq 0]$

$\Rightarrow$ Two solutions exist in the interval $[0, 2 π]$ .

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Trigonometrical Equations 3 Question 2

2. The number of solutions of the pair of equations 2sin2⁡θ−cos⁡2θ=0 and 2cos2⁡θ−3sin⁡θ=0 in the interval [0,2π] is

Answer:

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2. The number of solutions of the pair of equations $2 \sin^{2} θ - \cos 2 θ = 0$ and $2 \cos^{2} θ - 3 \sin θ = 0$ in the interval $[0, 2 π]$ is