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jonny [76]
3 years ago
7

What is the answer ?

Mathematics
1 answer:
Len [333]3 years ago
7 0

Answer:

Thus, option (c) is correct.

β = 61.5

Step-by-step explanation:

Given , \sin (\frac{x}{2}+20x)=\cos(2x+\frac{15x}{2}) , we have to solve for x, and then find the value of β ( β > α )

Consider \sin (\frac{x}{2}+20x)=\cos(2x+\frac{15x}{2}),

First solve for x ,

\Rightarrow \sin (\frac{x}{2}+20x)=\cos(2x+\frac{15x}{2})

\Rightarrow \sin (\frac{x+40x}{2})=\cos(\frac{4x+15x}{2})

Thus, \Rightarrow \sin (\frac{41x}{2})=\cos(\frac{19x}{2})

Also, \sin (90-\theta)=\cos \theta , we get,

Thus, \Rightarrow \cos (90-\frac{41x}{2})=\cos(\frac{19x}{2})

since, LHS = RHS thus, angle must be equal,

\Rightarrow 90-\frac{41x}{2}=\frac{19x}{2}

\Rightarrow 90=\frac{19x}{2}+\frac{41x}{2}

\Rightarrow 90=\frac{19x+41x}{2}

\Rightarrow 90=\frac{60x}{2}

\Rightarrow x=3

Thus, \frac{x}{2}+20x=\frac{3}{2}+20(3)=\frac{3}{2}+60=61.5 ,

Other angle can be found using angle sum property, as sum of angle of a triangle is 180°

Let third angle be y, then ,

90 + 61.5 + y = 180°

y = 180° - 151.5°

y = 28.5°

Since ( β > α ) ⇒ β= 61.5 and  α = 28.5

Thus, option (c) is correct.

⇒ β = 61.5


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