Mathematics Crash Course NDA & NA EE>Chapter 6 - Trigonometric Equations and Inequations>Exercise 1>Q 22

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If $\cos (α - β) = 1$ and $\cos (α + β) = \frac{1}{e}$ , where $α, β \in [- π, π]$ , then the number of ordered pairs $(α, β)$ is

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Important Questions on Trigonometric Equations and Inequations

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Mathematics Crash Course NDA & NA EE>Chapter 6 - Trigonometric Equations and Inequations>Exercise 1>Q 23

The number of solutions of the equation

\tan^{2} x - \sec^{10} x + 1 = 0

in

(0, 10)

is

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NDA & NA EE

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Mathematics Crash Course NDA & NA EE>Chapter 6 - Trigonometric Equations and Inequations>Exercise 1>Q 24

If

\sin (α + β) = 1

and

\sin (α - β) = \frac{1}{2}

,

(α, β \in (0, \frac{π}{2}))

then

\tan (α + 2 β) \tan (2 α + β)

is equal to

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Mathematics Crash Course NDA & NA EE>Chapter 6 - Trigonometric Equations and Inequations>Exercise 1>Q 25

The number of solutions of

\cos 2 θ = \sin θ

in

(0, 2 π)

is

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NDA & NA EE

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Mathematics Crash Course NDA & NA EE>Chapter 6 - Trigonometric Equations and Inequations>Exercise 1>Q 26

The smallest positive

x

satisfying the equation

\log_{\cos x} \sin x + \log_{\sin x} \cos x = 2

is

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NDA & NA EE

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Mathematics Crash Course NDA & NA EE>Chapter 6 - Trigonometric Equations and Inequations>Exercise 1>Q 27

The general solution of the equaiton

\sin^{100} x - \cos^{100} x = 1

is

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NDA & NA EE

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Mathematics Crash Course NDA & NA EE>Chapter 6 - Trigonometric Equations and Inequations>Exercise 1>Q 28

If

4 \sin^{2} θ = 1,

where

0 < θ < 2 π,

how many values does

θ

take

?

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NDA & NA EE

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Mathematics Crash Course NDA & NA EE>Chapter 6 - Trigonometric Equations and Inequations>Exercise 1>Q 29

If

\cot x + cosec x = \sqrt{3}

, then the value of

(x - \frac{π}{6})

which lies in

[0, 2 π)

is

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 6 - Trigonometric Equations and Inequations>Exercise 1>Q 30

If

\sin θ - \cos θ < 0,

then

θ

lies between