Express each of the following as the sum or difference of sines and cosines:

(i) 2 sin 3x cos x

(ii) 2 cos 3x sin 2x

(iii) 2 sin 4x sin 3x

(iv) 2 cos 7x cos 3x

Prove that :

i.

Show that:

i.

ii.

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

tan 20° tan 40° tan 60° tan 80° = 3

Prove that:

tan 20° tan 30° tan 40° tan 80° = 1

Prove that:

Prove that:

Show that

i. sin A sin (B – C) + sin B sin (C – A) + sin C sin (A – B) = 0

ii. sin (B – C) cos (A – D) + sin (C – A) cos(B – D) + sin(A – B) cos(C – D) = 0

Prove that:

Express each of the following as the product of sines and cosines:

i. sin 12x + sin 4x

ii. sin 5x – sin x

iii. cos 12x + cos 8x

iv. 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 :

Prove that :

sin 80° – cos 70° = cos 50°

Prove that :

sin 51° + cos 81° = cos 21°

Prove that:

i.

ii.

Prove that:

i.

ii. 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 :

Prove that :

Prove that :

Prove that :

Prove that :

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

i.

ii. cos (A + B + C) + cos (A – B + C) + cos (A + B – C) + cos (-A + B + C) = 4 cos A cos B cos C

prove that

If sin 2A = λ sin 2B, prove that:

Prove that:

i.

ii. sin(B– C)cos(A – D) + sin(C – A)cos(B – D) + sin(A – B)cos(C – D) = 0

prove that tan A tan B tan C tan D= -1

If cos (α + β) sin (γ + δ) = cos (α - β) sin (γ - δ), prove that cot α cot β cot γ = cot δ

If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y -x) cot θ

If cos (A + B) sin (C – D) = cos (A – B) sin (C + D), prove that tan A tan B tan C + tan D = 0

If (cos α + cos β)² + (sin α + sin β)² write the value of λ.

If sin A + sin B = α and cos A + cos B = β, then write the value of

If cos A = m cos B, then write the value of

Write the value of the expression

If and cos A + cos B = 1, then find the value of

Write the value of

If sin 2A = λ sin 2B, then write the value of

Write the value of

If cos (A + B) sin (C – D) = cos (A – B) sin (C + D), then write the value tan A tan B tan C.

Mark the Correct alternative in the following:

cos 40^o + cos 80^o + cos 160^o + cos 240^o =

Mark the Correct alternative in the following:

sin 163^o cos 347^o + sin 73^o sin 167^o =

Mark the Correct alternative in the following:

If and then

Mark the Correct alternative in the following:

The value of cos 52^o + cos 68^o + cos 172^o is

Mark the Correct alternative in the following:

The value of sin 78^o – sin 66^o – sin 42^o + sin 6^o is

Mark the Correct alternative in the following:

If sin α + sin β = a and cos α – cos β = b, then

Mark the Correct alternative in the following:

cos 35^o + cos 85^o + cos 155^o =

Mark the Correct alternative in the following:

The value of sin 50^o – sin 70^o + sin 10^o is equal to

Mark the Correct alternative in the following:

sin 47^o + sin 61^o – sin 11^o – sin 25^o is equal to

Mark the Correct alternative in the following:

If cos A = m cos B, then =

Mark the Correct alternative in the following:

If A, B, C are in A.P., then

Mark the Correct alternative in the following:

If sin (B + C – A), sin (C + A – B), sin (A + B – C) are in A.P., then cot A, cot B, cot C are in

Mark the Correct alternative in the following:

If then sin 3x + sin 3y =

Mark the Correct alternative in the following:

If and then
α + β is equal to