Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 24

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The number of solution(s) of the equation, $e^{\cos^{2} x} - e^{- \cos^{2} x} + 4 = 0$ in $[0, 2 π]$ is/are:

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Important Questions on Trigonometric Functions and Identities

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JEE Main

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 25

The value

y

for which the equation

4 \sin x + 3 \cos x = y^{2} - 6 y + 14

has a real solution is/are:

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 26

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 1 - Trigonometric Functions and Identities>Objective Questions>Q 27

\sin x + \sin y = y^{2} - y + a

will have no solution in

x

and

y

if

a

belongs to:

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 28

If

x \cos α + y \sin α = x \cos β + y \sin β = 2 a

, then

\cos α \cdot \cos β

is

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 29

The number of roots of the equation,

x \sin x = 1

in the interval

0 < x < 2 π

is

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 30

If

\tan θ_{1}, \tan θ_{2}, \tan θ_{3}, \tan θ_{4}

are the roots of the equation

x^{4} - x^{3} \sin 2 β + x^{2} \cos 2 β - x \cos β - \sin β = 0

, then

\tan (θ_{1} + θ_{2} + θ_{3} + θ_{4})

is equal to:

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 31

If

f (x) = [\cos x \cos (x + 2) - \cos^{2} (x + 1)]

, where

[.]

denotes the greatest integer function. Then the solution of the equation $f (x) = x$ is

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 1 - Trigonometric Functions and Identities>Objective Questions>Q 32

If

[\cos x] + [\sin x + 1] = 0

, then the value of

x

satisfying, where

x \in [0, 2 π]

and

[.]

represents the greatest integer function.