TRIGONOMETRY: "The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth."
Example:
If xcosθ - ysinθ = a, xsinθ + ycos θ = b, prove that x^{2}+y^{2}=a^{2}+b^{2}.
Ans: xcosθ - y sinθ = a xsinθ + y cosθ = b Squaring and adding x^{2}+y^{2}=a^{2}+b^{2}.