prove-that-cos-2-a-sin-2-b-sin-acos-a-sin-bcos-b-cot-a-b-

Question Number 82879 by jagoll last updated on 25/Feb/20

prove that

\frac{\cos^{2} a + \sin^{2} b}{\sin acos a + \sin bcos b} = \cot (a + b)

Commented by mahdi last updated on 25/Feb/20

problem :

f o r a = 0 b = 30 \Rightarrow \frac{\cos^{2} a + \sin^{2} b}{\sin acos a + \sin bcos b} = \frac{1 + 0.25}{0 + \frac{\sqrt{3}}{4}} = \frac{5 \sqrt{3}}{3}

a n d c o t (0 + 30) = \sqrt{3}

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