Question

What is the answer ?

Answer 1

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