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 
$$\tan x\tan (\frac{\pi }{3}-x)\tan (\frac{\pi }{3}+x)=\tan 3x$$

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:
$$\sin \frac{5\pi }{18}-\cos \frac{4\pi }{9}=\sqrt{3}\sin \frac{\pi }{9}$$

Prove that:

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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:
 ${\displaystyle \sin A+\sin 2A+\sin 4A+\sin 5A=4\cos \left(\frac{A}{2}\right)\cos \left(\frac{3A}{2}\right)\sin 3A}$

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:

Prove that:

Prove that:

Prove that:

Prove that:

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

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

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