Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A\(\rightarrow\)B for each of the following:
neither one- to -one and nor onto.

Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A\(\rightarrow\)B for each of the following:
not one-to-one but onto.

Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A\(\rightarrow\)B for each of the following:
one-to-one but not onto.

Find the largest possible domain of the real valued function f(x) =\(\frac { \sqrt { 4-{ x }^{ 2 } } }{ \sqrt { { x }^{ 2 }-9 } } \)

Prove that \(\frac { sin4x+sin2x }{ cos4x+cos2x } =tan3x\)

Prove that \(1+cos2x+cos4x+cos6x=4cosx\ cos2x\ cos3x\)

Prove that \(sin\frac { \theta }{ 2 } sin\frac { 7\theta }{ 2 } +sin\frac { 3\theta }{ 2 } sin\frac { 11\theta }{ 2 } =sin2\theta sin5\theta \)

In a ∆ABC, prove that (a² - b² + c²) tan B = (a² + b² - c²) tan C

If A + B + C = \(\pi\), prove the following
i. cos A + cos B + cos C = 1 + 4 sin \(({A\over 2})\) sin \(({B\over 2})\) sin \(({C\over 2})\)
ii. sin \(({A\over 2})sin({B\over2})sin({C\over 2})\le{1\over 8}\)
iii. 1 < cos A + cos B + cos C \(\le\frac{3}{2}\)

In a triangle  ABC, prove that \({a^2+b^2\over a^2+c^2}={1+cos(A-B)cos C\over 1+cos (A-C)cos B}\)

Using Heron's formula, show that the equilateral triangle has the maximum area for any fixed perimeter. [Hint: In xyz \(\le\)  k, maximum occurs when x = y = z]

A ray of light coming from the point (1, 2)is reflected at a point A on the x-axis and it passes through the point (5, 3). Find the co-ordinates of the point A.

Find the distance of the line 4x - y = 0 from the point p( 4,1) measured along the line making an angle of 135° with the positive x-axis.