Question : If $\sin 3x=\cos(3x-45^{\circ}), 0^{\circ}<3x<90^{\circ}$, then $x$ is equal to:
Option 1: $45^\circ$
Option 2: $22.5^\circ$
Option 3: $35^\circ$
Option 4: $27.5^\circ$
Answer (1)
23rd Jan, 2024
Correct Answer: $22.5^\circ$
Solution :
Given: $\sin 3x = \cos(3x - 45^\circ)$
We know that,
$\sin \theta = \cos(90^\circ - \theta)$
⇒ $\sin 3x = \sin(90^\circ - (3x- 45^\circ))$
⇒ $3x = 90^\circ - 3x+45^\circ$
⇒ $6x = 135^\circ$
⇒ $x = 22.5^\circ$
Hence, the correct answer is $22.5^\circ$.
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