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Question Number 46814 by peter frank last updated on 31/Oct/18

	Answered by tanmay.chaudhury50@gmail.com last updated on 01/Nov/18
	$cosθ=((OP^2 +OQ^2 −PQ^2 )/(2×OP×OQ)) =(((a^2 +b^2 )+(c^2 +d^2 )−{(a−c)^2 +(b−d)^2 })/(2×(√(a^2 +b^2 )) ×(√(c^2 +d^2 )) )) =((ac+bd)/((√(a^2 +b^2 )) ×(√(c^2 +d^2 )) ))$
	$c o s θ = \frac{{O P}^{2} + {O Q}^{2} - {P Q}^{2}}{2 \times O P \times O Q}$ $= \frac{(a^{2} + b^{2}) + (c^{2} + d^{2}) - {{(a - c)}^{2} + {(b - d)}^{2}}}{2 \times \sqrt{a^{2} + b^{2}} \times \sqrt{c^{2} + d^{2}}}$ $= \frac{a c + b d}{\sqrt{a^{2} + b^{2}} \times \sqrt{c^{2} + d^{2}}}$
	Commented by peter frank last updated on 01/Nov/18

	$thank you$
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