RD Sharma solutions for Mathematics [English] Class 11 chapter 8 - Transformation formulae [Latest edition]

Express the following as the sum or difference of sines and cosines:
2 sin 3x cos x

Express the following as the sum or difference of sines and cosines:
2 cos 3x sin 2xa

Express the following as the sum or difference of sines and cosines:
2 sin 4x sin 3x

Express the following as the sum or difference of sines and cosines:
 2 cos 7x cos 3x

Prove that:

Prove that:

Prove that: 

Show that :

Show that :

Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]

Prove that:
cos 40° cos 80° cos 160° = \[- \frac{1}{8}\]

Prove that:
 sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]

Prove that:
cos 20° cos 40° cos 80° = \[\frac{1}{8}\]

Prove that:
tan 20° tan 40° tan 60° tan 80° = 3

Prove that tan 20° tan 30° tan 40° tan 80° = 1.

Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]

Prove that:
 sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]

Show that:
sin A sin (B − C) + sin B sin (C − A) + sin C sin (A − B) = 0

Show that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0

Prove that 
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]

If α + β = \[\frac{\pi}{2}\], show that the maximum value of cos α cos β is \[\frac{1}{2}\].

Express each of the following as the product of sines and cosines:
sin 12x + sin 4x

Express each of the following as the product of sines and cosines:
sin 5x − sin x

Express each of the following as the product of sines and cosines:
 cos 12x + cos 8x

Express each of the following as the product of sines and cosines:
 cos 12x - cos 4x

Express each of the following as the product of sines and cosines:
sin 2x + cos 4x

Prove that:
sin 38° + sin 22° = sin 82°

Prove that:
 cos 100° + cos 20° = cos 40°

Prove that:
sin 50° + sin 10° = cos 20°

Prove that:
 sin 23° + sin 37° = cos 7°

Prove that:
sin 105° + cos 105° = cos 45°

Prove that:
sin 40° + sin 20° = cos 10°

Prove that:
 cos 55° + cos 65° + cos 175° = 0

Prove that:
 sin 50° − sin 70° + sin 10° = 0

Prove that:
 cos 80° + cos 40° − cos 20° = 0

Prove that:
cos 20° + cos 100° + cos 140° = 0

Prove that:
\[\sin\frac{5\pi}{18} - \cos\frac{4\pi}{9} = \sqrt{3} \sin\frac{\pi}{9}\]

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Prove that:
sin 47° + cos 77° = cos 17°

Prove that:
cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A

Prove that: 
cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A

Prove that:
 `sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`

Prove that:
sin 3A + sin 2A − sin A = 4 sin A cos \[\frac{A}{2}\] \[\frac{3A}{2}\]

Prove that:

cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −\[\frac{3}{4}\]

Prove that:

Prove that:

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Prove that:

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Prove that:

Prove that:
cos (A + B + C) + cos (A − B + C) + cos (A + B − C) + cos (− A + B + C) = 4 cos A cos Bcos C

If cosec A + sec A = cosec B + sec B, prove that tan A tan B = \[\cot\frac{A + B}{2}\].

Prove that:

Prove that:
 sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0

If \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]

If \[m \sin\theta = n \sin\left( \theta + 2\alpha \right)\], prove that \[\tan\left( \theta + \alpha \right) \cot\alpha = \frac{m + n}{m - n}\]

If (cos α + cos β)² + (sin α + sin β)² = \[\lambda \cos^2 \left( \frac{\alpha - \beta}{2} \right)\], write the value of λ. 

Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].

If sin A + sin B = α and cos A + cos B = β, then write the value of tan \[\left( \frac{A + B}{2} \right)\].

If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].

Write the value of the expression \[\frac{1 - 4 \sin 10^\circ \sin 70^\circ}{2 \sin 10^\circ}\]

If A + B = \[\frac{\pi}{3}\] and cos A + cos B = 1, then find the value of cos \[\frac{A - B}{2}\].

Write the value of \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]

If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]

Write the value of \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]

cos 40° + cos 80° + cos 160° + cos 240° =

sin 163° cos 347° + sin 73° sin 167° =

If sin 2 θ + sin 2 ϕ = \[\frac{1}{2}\] and cos 2 θ + cos 2 ϕ = \[\frac{3}{2}\], then cos² (θ − ϕ) =

The value of cos 52° + cos 68° + cos 172° is

The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.

If sin α + sin β = a and cos α − cos β = b, then tan \[\frac{\alpha - \beta}{2}\]=

cos 35° + cos 85° + cos 155° =

The value of sin 50° − sin 70° + sin 10° is equal to

sin 47° + sin 61° − sin 11° − sin 25° is equal to

If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=

If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=

If sin (B + C − A), sin (C + A − B), sin (A + B − C) are in A.P., then cot A, cot B and cot Care in

If sin x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =

If \[\tan\alpha = \frac{x}{x + 1}\] and