Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

Prove that: `(cos x  + cos y)^2 + (sin x - sin y )^2 =  4 cos^2  (x + y)/2`

Prove that: `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2  (x - y)/2`

Prove that: sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

Prove that: `((sin 7x + sin 5x) + (sin 9x + sin 3x))/((cos 7x + cos 5x) + (cos 9x + cos 3x)) = tan 6x`

Prove that: sin 3x + sin 2x – sin x = 4sin x `cos  x/2 cos  (3x)/2`

Find the modulus and the argument of the complex number  `z = – 1 – isqrt3`

Find the modulus and the argument of the complex number `z =- sqrt3 + i`

Convert the given complex number in polar form `sqrt3 + i`

Convert the following in the polar form:

`(1+7i)/(2-i)^2`

Convert the following in the polar form:

`(1+3i)/(1-2i)`

Solve the following system of inequalities graphically: 3x + 2y ≤ 12, x ≥ 1, y ≥ 2

Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12

Solve the following system of inequalities graphically: x + y≥ 4, 2x – y > 0