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

If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)

Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1

Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`

If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α

Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`

Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`

Find the value of cos 2A, A lies in the first quadrant, when tan A  `16/63`

If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`

If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`

If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`

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