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

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

If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos  "A"/2 cos  "B"/2 sin  "C"/2`

If A + B + C = 180°, prove that sin²A + sin²B + sin²C = 2 + 2 cos A cos B cos C

If A + B + C = 180°, prove that sin²A + sin²B − sin²C = 2 sin A sin B cos C

If A + B + C = 180°, prove that `tan  "A"/2  tan  "B"/2 + tan  "B"/2 tan  "C"/2 + tan  "C"/2 tan  "A"/2` = 1

If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos  "A"/2 cos  "B"/2 cos  "C"/2`

If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C

If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s  sin(s – C) = sin A sin B

If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`

If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C

If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C