Mathematics
02.09.2020 06:54
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101EXPERIENCE
101EXPERIENCE
4,5(69 marks)

 see proof below

Step-by-step explanation:

Use the following Sum Identities:

cos (A + B) = cosA · cosB - sinA · sinB

sin (A + B) =  sinA · cos B - cosA · sinB

Use the Unit Circle to evaluate the following:

cos 30 = √3/2                            sin 30 = 1/2

cos 45 = √2/2                            sin 45 = √2/2

cos 120 = -1/2                             sin 120 = √3/2

cos 240 = -1/2                             sin 240 = -√3/2                        

cos 315 = √2/2                           sin 315 = -√2/2        

cos 330 = √3/2                          sin 330 = -1/2

Proof LHS → RHS

\text{LHS:}\qquad \qquad \dfrac{\cos 285+\cos 345}{\sin 435-\sin 375}

\text{Expand:}\qquad \quad \dfrac{\cos (240+45)+\cos (315+30)}{\sin (315+120)-\sin (330+45)}

\text{Sum Identity:}\qquad \dfrac{\cos 240\cdot \cos 45-\sin 240\cdot 45+\cos 315\cdot \cos 30-\sin 315\cdot 30}{\sin 315\cdot \cos 120+\cos315\cdot \sin 120-(\sin330\cdot \cos45+\cos 330\cdot \sin 45) }

\text{Unit Circle:}\quad \dfrac{(\frac{-1}{2}\cdot \frac{\sqrt2}{2})-(\frac{-\sqrt3}{2}\cdot \frac{\sqrt2}{2})+(\frac{\sqrt2}{2}\cdot \frac{\sqrt3}{3})-(\frac{-\sqrt2}{2}\cdot \frac{1}{2})}{(\frac{-\sqrt2}{2}\cdot \frac{-1}{2})+(\frac{\sqrt2}{2}\cdot \frac{\sqrt3}{2)}-(\frac{-1}{2}\cdot \frac{\sqrt2}{2})-(\frac{\sqrt3}{2}\cdot \frac{\sqrt2}{2})}

\text{Simplify:}\qquad \dfrac{-\sqrt2+\sqrt6+\sqrt6+\sqrt2}{\sqrt2+\sqrt6+\sqrt2-\sqrt6}\qquad =\dfrac{2\sqrt6}{2\sqrt2}\qquad =\sqrt3

LHS = RHS: \sqrt3 = \sqrt3\qquad \checkmark


Please someone help me...
Braxtonw875
Braxtonw875
4,4(26 marks)

No sheee

Step-by-step explanation:

N

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