Question

Find x, if sin 3x = cos (x – 30°), 0  3x  90°.​

Answer 1

Given,

$\longrightarrow\sin(3x)=\cos(x-30^o)$

Since $\sin\theta=\cos(90^o-\theta),$

$\longrightarrow\cos(90^o-3x)=\cos(x-30^o)$

Taking cos inverse,

$\longrightarrow 90^o-3x=x-30^o$

$\longrightarrow4x=120^o$

$\longrightarrow\underline{\underline{x=30^o}}$

where $3x=90^o\in[0^0,\ 90^o].$

Let's check if it's true.

$\longrightarrow \sin(3x)=\sin(3\times30^o)=\sin90^o=1$

$\longrightarrow \cos(x-30^o)=\cos(30^o-30^o)=\cos0^o=1$

Therefore,

$\longrightarrow\sin(3x)=\cos(x-30^o)$

Hence it's true.

Answer 2

Answer:

30⁰ is correct

Step-by-step explanation:

sin 3x = cos(x-30⁰)

sin 3x = sin [90⁰-(x-30⁰)] [sin x = cos(90⁰-x)]

3x = -x+120⁰

4x = 120⁰

x = 30⁰