HSC Science इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Prove that cos 5θ = 16 cos⁵θ – 20 cos³θ + 5 cos θ

Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`

If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2

Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4

Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ

Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`

Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2ⁿθ) = tan 2ⁿθ

Prove that `32(sqrt(3)) sin  pi/48  cos  pi/48  cos  pi/24  cos  pi/12  cos  pi/6` = 3

Express the following as a sum or difference
sin 35° cos 28°

Express the following as a sum or difference
sin 4x cos 2x

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