Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

sin 163° cos 347° + sin 73° sin 167° =

If sin 2 θ + sin 2 ϕ = \[\frac{1}{2}\] and cos 2 θ + cos 2 ϕ = \[\frac{3}{2}\], then cos² (θ − ϕ) =

The value of cos 52° + cos 68° + cos 172° is

The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.

If sin α + sin β = a and cos α − cos β = b, then tan \[\frac{\alpha - \beta}{2}\]=

cos 35° + cos 85° + cos 155° =

The value of sin 50° − sin 70° + sin 10° is equal to

sin 47° + sin 61° − sin 11° − sin 25° is equal to

If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=

If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=

If sin (B + C − A), sin (C + A − B), sin (A + B − C) are in A.P., then cot A, cot B and cot Care in

If sin x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =

If \[\tan\alpha = \frac{x}{x + 1}\] and 

Find the value of tan22°30′. `["Hint:"  "Let" θ = 45°, "use" tan  theta/2 = (sin  theta/2)/(cos  theta/2) = (2sin  theta/2 cos  theta/2)/(2cos^2  theta/2) = sintheta/(1 + costheta)]`

If secx cos5x + 1 = 0, where 0 < x ≤ `pi/2`, then find the value of x.

The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is ______.

Equation of a circle which passes through (3, 6) and touches the axes is ______.

Equation of the circle with centre on the y-axis and passing through the origin and the point (2, 3) is ______.

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is ______.

`lim_(n -> oo) (1 + 2 + 3 + ... + n)/n^2`, n ∈ N, is equal to ______.