Answer :
Step-by-step explanation:
[tex] \sin(2x)= \cos (x+30°) \\ \\ \therefore \: \cos(90 \degree - 2x)= \cos (x+30°)\\
\{\because \sin \theta = \cos(90°-\theta)\}
\\ \\ \therefore \: 90\degree - 2x = x+30° \\ \\ \therefore \: 90\degree - 30\degree = x + 2x \\ \\ \therefore \: 60\degree =3 x\\ \\ \therefore \: x = \frac{60\degree}{3} \\ \\ \huge \red{ \boxed{ \therefore \: x = 20 \degree }}[/tex]
The value of sine angle is always equal to the value of 90 - cosine angle. Thus, the value of x is 20.
Trigonometric ratios are used only in right angled triangles to determine the values of angles made between the sides of the triangle.
We need to determine the value of variable x.
The given expression is mentioned below.
[tex]\sin(2x)=\cos (x+30)^\circ\\[/tex]
Now, to calculate the value of the variable x, the whole expression must be converted into the single trigonometric ratio.
Therefore, apply the above statement and solve the expression further for the value of x.
[tex]\begin{aligned}\sin(2x)&=\sin (90-(x+30))^\circ\\2x&=90-x-30\\3x&=60\\x&=20 \end{aligned}[/tex]
Thus, the value of x is 20.
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