HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Express the following as a sum or difference
2 sin 10θ  cos 2θ

Express the following as a sum or difference
cos 5θ  cos 2θ

Express the following as a sum or difference
sin 5θ  sin 4θ

Express the following as a product
sin 75° sin 35°

Express the following as a product
cos 65° + cos 15°

Express the following as a product
sin 50° + sin 40°

Express the following as a product
cos 35° – cos 75°

Show that sin 12° sin 48° sin 54° = `1/8`

Show that `cos  pi/15  cos  (2pi)/15  cos  (3pi)/15  cos  (4pi)/15  cos  (5pi)/15  cos  (6pi)/15  cos  (7pi)/15 = 1/128`

Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x

Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1

Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)

Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x

Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x

Prove that `sin  theta/2 sin  (7theta)/2 + sin  (3theta)/2 sin  (11theta)/2` =  sin 2θ sin 5θ

Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`

Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x  cos 7x)` = tan 4x

Prove that `(sin(4"A" - 2"B") + sin(4"B" - 2"A"))/(cos(4"A" - 2"B") + cos(4"B" - 2"A"))` = tan(A + B)

Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`

If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C