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

Prove that sin²(A + B) – sin²(A – B) = sin2A sin2B

Prove that cos 8θ cos 2θ = cos²5θ – sin²3θ

Show that cos² A + cos² B – 2 cos A cos B cos(A + B) = sin²(A + B)

If cos(α – β) + cos(β – γ) + cos(γ – α) = `- 3/2`, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0

Show that tan(45° + A) =  `(1 + tan"A")/(1 - tan"A")`

Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`

Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`

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