Question

Given A=60 and B=30,prove that Cos (A+B) =Cos A Cos B= sin A sin B​

Answer 1

Answer:

Here is the answer.

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Step-by-step explanation:

Given that,

A = 60° and B = 30°

L.H.S

$cos(A+B) \\ = cos(60+30) \\ = cos(90) \\ = 1$

R.H.S

$cosAcosB - sinAsinB \\ = cos60cos30 - sin60sin30 \\ = \frac{1}{2} \times \frac{ \sqrt{3} }{2} - \frac{ \sqrt{3} }{2} \times \frac{1}{2} \\ = \frac{ \sqrt{3} }{4} - \frac{ \sqrt{3} }{4} \\ = 0$

L.H.S = R.H.S (proved)