TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 9

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Mathematics

IMPORTANT

Earn 100

The number of solutions of the equation $\sin 2 x + \sin 3 x + \sin 4 x + \dots + \sin n x = n - 1$ is

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Important Questions on Trigonometric Equations and Inequations

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 10

If

\sin x + \cos x = \sqrt{y + \frac{1}{y}}, x \in (0, π)

, then

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 11

Let

[x]

denote the greatest integer

\leq x

, the equation

\sin x = [1 + \sin x] + [1 - \cos x]

has

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 12

If

0 \leq θ \leq 4 π

and

x \in R

then

\sin θ + \sqrt{3} \cos θ = 6 x - x^{2} - 11

holds for

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 13

The value of

θ

lying between

0

and

\frac{π}{2}

and satisfying the equation

|\begin{matrix} 1 + \sin^{2} θ & \cos^{2} θ & 4 \sin 4 θ \\ \sin^{2} θ & 1 + \cos^{2} θ & 4 \sin 4 θ \\ \sin^{2} θ & \cos^{2} θ & 1 + 4 \sin 4 θ \end{matrix}| = 0

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 14

The equation whose roots are nth power of the roots of the equation,

x^{2} - 2 x \cos θ + 1 = 0,

is given by

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 15

For solution of the system of equations

\tan^{2} x + \cot^{2} x = 2 \sin^{2} y

and

\sin^{2} y + \cos^{2} z = 1

MEDIUM

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 3

If

3 \sin x + 4 \cos x = 5

, then the value of

90 \tan^{2} (\frac{x}{2}) - 60 \tan (\frac{x}{2}) + 110

is equal to

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Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 4

If

x

and

y

are the solutions of the equation

12 \sin x + 5 \cos x = 2 y^{2} - 8 y + 21

, the value of

144 \cot (\frac{x y}{2})

is