If \(\sin 2\theta=\cos 40^\circ\), then the smallest positive value of \(\theta\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 25°
The sine of an angle equals the cosine of its complement: \(\sin\theta=\cos(90^\circ-\theta)\). So \(\cos40^\circ\) can be written as a sine.
\(\cos40^\circ=\sin(90^\circ-40^\circ)=\sin50^\circ\)
\(\sin2\theta=\sin50^\circ\), so \(2\theta=50^\circ\) for the smallest positive value
\(\theta=25^\circ\)