SATHEE: Trigonometrical Ratios and Identities 1 Question 29

Trigonometrical Ratios and Identities 1 Question 29

29. The number of all possible values of $θ$ , where $0 < θ < π$ , for which the system of equations

$\begin{aligned} (y + z) \cos 3 θ & = (x y z) \sin 3 θ \\ x \sin 3 θ & = \frac{2 \cos 3 θ}{y} + \frac{2 \sin 3 θ}{z} \end{aligned}$

and $(x y z) \sin 3 θ = (y + 2 z) \cos 3 θ + y \sin 3 θ$ have a solution $(x_{0}, y_{0}, z_{0})$ with $y_{0} z_{0} \neq 0$ , is ……

(2010)

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Solution:

Given equations can be written as

$\begin{aligned} x \sin 3 θ - \frac{\cos 3 θ}{y} - \frac{\cos 3 θ}{z} & = 0 \\ x \sin 3 θ - \frac{2 \cos 3 θ}{y} - \frac{2 \sin 3 θ}{z} & = 0 \end{aligned}$

and $x \sin 3 θ - \frac{2}{y} \cos 3 θ - \frac{1}{z} (\cos 3 θ + \sin 3 θ) = 0$

Eqs. (ii) and (iii), implies

$\begin{aligned} 2 \sin 3 θ & = \cos 3 θ + \sin 3 θ \\ ∴ & \sin 3 θ & = \cos 3 θ \\ \Rightarrow & \tan 3 θ & = 1 \\ 3 θ & = \frac{π}{4}, \frac{5 π}{4}, \frac{9 π}{4} \\ or & θ & = \frac{π}{12}, \frac{5 π}{12}, \frac{9 π}{12} \end{aligned}$

Trigonometrical Ratios and Identities 1 Question 29

29. The number of all possible values of $θ$ , where $0 < θ < π$ , for which the system of equations

Solution:

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Trigonometrical Ratios and Identities 1 Question 29

29. The number of all possible values of θ, where 0<θ<π, for which the system of equations

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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29. The number of all possible values of $θ$ , where $0 < θ < π$ , for which the system of equations