Mathematics Crash Course MHT-CET>Chapter 3 - Trigonometric Ratios and Identities>Exercise 1>Q 63

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$\sin^{2} \frac{π}{18} + \sin^{2} \frac{π}{9} + \sin^{2} \frac{7 π}{18} + \sin^{2} \frac{4 π}{9}$ is equal to

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Important Questions on Trigonometric Ratios and Identities

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 3 - Trigonometric Ratios and Identities>Exercise 1>Q 64

If

x = \cos α + \cos β - \cos (α + β)

and

y = 4 \sin \frac{α}{2} \sin \frac{β}{2} \cos (\frac{α + β}{2})

, then

(x - y)

equals

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 3 - Trigonometric Ratios and Identities>Exercise 1>Q 65

In

∆ A B C

if

\tan \frac{A}{2}

,

\tan \frac{B}{2}

,

\tan \frac{C}{2}

are in A.P., then

\cos A, \cos B, \cos C

are in

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 3 - Trigonometric Ratios and Identities>Exercise 1>Q 66

The expression

\frac{1 + \sin 2 α}{\cos (2 α - 2 π) . \tan (α - \frac{3 π}{4})} - \frac{1}{4} \sin 2 α \{\cot \frac{α}{2} + \cot (\frac{3 π}{2} + \frac{α}{2})\}

is equal to

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Mathematics Crash Course MHT-CET>Chapter 3 - Trigonometric Ratios and Identities>Exercise 1>Q 67

If

cosec θ = \frac{p + q}{p - q},

then

\cot (\frac{π}{4} + \frac{θ}{2}) =

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Mathematics Crash Course MHT-CET>Chapter 3 - Trigonometric Ratios and Identities>Exercise 1>Q 68

The value of $2 (\cos^{2} 20 ° + \cos^{2} 140 ° + \cos^{2} 100 °)$ is

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Mathematics Crash Course MHT-CET>Chapter 3 - Trigonometric Ratios and Identities>Exercise 1>Q 69

If

A

and

B

are positive acute angles satisfying the equalities

3 \cos^{2} A + 2 \cos^{2} B = 4 & \frac{3 \sin A}{\sin B} = \frac{2 \cos B}{\cos A}

, then

A + 2 B

is equal to

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 3 - Trigonometric Ratios and Identities>Exercise 1>Q 70

The value of $x$ satisfying the equation $x = \sqrt{2 + \sqrt{2 - \sqrt{2 + x}}}$

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 3 - Trigonometric Ratios and Identities>Exercise 1>Q 71

If

P_{n} = \cos^{n} θ + \sin^{n} θ

, then

2 P_{6} - 3 P_{4} + 1 =