Principle of Mathematical Induction

Principle of Mathematical Induction

Question

In any quadrilateral ABCD, show that sin (A + B) + sin (C + D) = 0.

Answer

ABCD is a quadrilateral
rightwards double arrow            space space space straight A plus straight B plus straight C plus straight D space equals space 360 degree space equals space 2 straight pi
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rightwards double arrow           sin left parenthesis straight A plus straight B right parenthesis space equals space sin left square bracket 2 straight pi space minus space left parenthesis straight C space plus straight D right parenthesis right square bracket
x is quadrant IV means sinx is -ve.
∴              sin (A + B) = sin[2straight pi - (C + D)] = - sin (C + D)
Hence, sin (A + B) + sin (C + D) = 0

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