Beta Question Bank for Engineering: Mathematics>Chapter 12 - Trigonometric Ratios, Functions and Identities>EXERCISE-1>Q 17

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IMPORTANT

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The tangents of two acute angles are $3$ and $2$ . The sine of twice their difference is -

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Important Questions on Trigonometric Ratios, Functions and Identities

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 12 - Trigonometric Ratios, Functions and Identities>EXERCISE-1>Q 18

If

\frac{\sin 2 α - \sin 3 α + \sin 4 α}{\cos 2 α - \cos 3 α + \cos 4 α} = \tan k α

is an identity then the value of

k

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 12 - Trigonometric Ratios, Functions and Identities>EXERCISE-1>Q 19

Exact value of

\cos 20 ° + 2 \sin^{2} 55 ° - \sqrt{2} \sin 65 °

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 12 - Trigonometric Ratios, Functions and Identities>EXERCISE-1>Q 20

If

\cos (θ + ϕ) = m \cos (θ - ϕ)

then

\tan θ

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 12 - Trigonometric Ratios, Functions and Identities>EXERCISE-1>Q 21

If

\sin θ + \cos e c θ = 2

, then the value of

\sin^{8} θ + \cos e c^{8} θ

is equal to -

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 12 - Trigonometric Ratios, Functions and Identities>EXERCISE-1>Q 22

If the expression

4 \sin 5 α \cos 3 α \cos 2 α

is expressed as the sum of three sines then two of them are

\sin 4 α

and

\sin 10 α

. The third one is -

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 12 - Trigonometric Ratios, Functions and Identities>EXERCISE-1>Q 23

The expression

3 [\sin^{4} (\frac{3 π}{2} - α) + \sin^{4} (3 π + α)] - 2 [\sin^{6} (\frac{π}{2} + α) + \sin^{6} (5 π - α)]

when simplified is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 12 - Trigonometric Ratios, Functions and Identities>EXERCISE-1>Q 24

If

\cos θ = \frac{1}{2} (a + \frac{1}{a})

then

\cos 3 θ

in terms of

' a'

=

EASY

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 12 - Trigonometric Ratios, Functions and Identities>EXERCISE-1>Q 25

\frac{1}{\cos 290^{0}} + \frac{1}{\sqrt{3} \sin 250^{0}} =