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

Find a quadratic equation whose roots are sin 15° and cos 15°

Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`

Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`

Prove that sin(30° + θ) + cos(60° + θ) = cos θ

If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y

Prove that sin 105° + cos 105° = cos 45°

Prove that sin 75° – sin 15° = cos 105° + cos 15°

Show that tan 75° + cot 75° = 4

Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)

Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z

If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx

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

Prove that cos(A + B) cos(A – B) = cos²A – sin²B = cos²B – sin²A

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")`