Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 2 - Trigonometric Equations and Inequations>Objective Questions>Q 8

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IMPORTANT

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Total number of solutions of $[\sin x] + \cos x = 0$ ; where $[.]$ denotes the greatest integer function, for $x \in [0, 2 π]$ , is :

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Important Questions on Trigonometric Equations and Inequations

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JEE Main

IMPORTANT

Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 2 - Trigonometric Equations and Inequations>Objective Questions>Q 9

Consider the equation

\sin 3 α = 4 \sin α . \sin (x + α) \sin (x - α), α \in (0, π)

and

x \in (0, 2 π),

then for

x

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 2 - Trigonometric Equations and Inequations>Objective Questions>Q 10

The number of points inside or on the circle

x^{2} + y^{2} = 4

satisfying

\tan^{4} x + \cot^{4} x + 1 = 3 \sin^{2} y,

is:

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 2 - Trigonometric Equations and Inequations>Objective Questions>Q 11

The most general solution of

\tan θ = - 1

and

\cos θ = \frac{1}{\sqrt{2}}

is

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 2 - Trigonometric Equations and Inequations>Objective Questions>Q 12

The most general value of

θ

which satisfy both the equations

\cos θ = - \frac{1}{\sqrt{2}}

and

\tan θ = 1,

is :

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 2 - Trigonometric Equations and Inequations>Objective Questions>Q 13

The general solution of the equation;

\cos (x) \cos (6 x) = - 1

is

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JEE Main

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 2 - Trigonometric Equations and Inequations>Objective Questions>Q 14

The equation

\sin^{4} x + \cos^{4} x + \sin 2 x + α = 0

is solvable for:

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 2 - Trigonometric Equations and Inequations>Objective Questions>Q 15

The number of pairs

(x, y)

satisfy equations

\sin x + \sin y = \sin (x + y)

and

| x | + | y | = 1,

is

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IMPORTANT

Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 2 - Trigonometric Equations and Inequations>Objective Questions>Q 16

If

A

and

B

are acute angles satisfying the equations

3 \sin^{2} A + 2 \sin^{2} B = 1

and

3 \sin 2 A - 2 \sin 2 B = 0,

then

(A + 2 B)

is