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Lina20 [59]
3 years ago
10

Solve each equation for 0≤x≤360 cos(x+45°)+cos(x-45°)= √2

Mathematics
1 answer:
andreev551 [17]3 years ago
7 0

Answer:

0°

360°

Step-by-step explanation:

We want to solve the equation,

\cos(x + 45)  +  \cos(x  - 45)  =  \sqrt{2}

We expand using trigonometric identities to get;

\cos(x) \cos( 45)   -  \sin(x)  \sin(45) +  \cos(x) \cos( 45)    +  \sin(x)  \sin(45)  =  \sqrt{2}

\frac{ \sqrt{2} }{2}  \cos(x)   -   \frac{ \sqrt{2} }{2} \sin(x) +  \frac{ \sqrt{2} }{2}  \cos(x)    +  \frac{ \sqrt{2} }{2} \sin(x)   =  \sqrt{2}

Simplify;

\cos(x)   -  \sin(x) + \cos(x)    +  \sin(x)   =  2

Simplify;

\cos(x)  + \cos(x)  =  2

Add

2\cos(x)  =  2

Divide by 2

\cos(x)  = 1

Take cosine inverse;

In the

x =  \cos^{ - 1} ( 1) =0\degree

Also in the 3rd quadrant cosine ratio is positive.

x = 360-0= 360 \degree

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