If 2 = 40^, then the smallest positive value of is : Option 1: 25^ Option 2: 20^ Option 3: 40^ Option 4: 30^

Answer: 25^. Solution: We use the identity x = (90^ - x). So 40^ = 50^. Thus 2 = 50^, giving 2 = 50^, hence = 25^.

Geometry

Trigonometry

Easy

If $\sin 2\theta = \cos 40^\circ$ , then the smallest positive value of $\theta$ is :

$25^\circ$

$20^\circ$

$40^\circ$

$30^\circ$

✅ Correct Option: 1

We use the identity $\cos x = \sin(90^\circ - x)$ .

So $\cos 40^\circ = \sin 50^\circ$ .

Thus $\sin 2\theta = \sin 50^\circ$ , giving $2\theta = 50^\circ$ , hence $\theta = 25^\circ$ .

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If sin⁡2θ=cos⁡40∘\sin 2\theta = \cos 40^\circsin2θ=cos40∘, then the smallest positive value of θ\thetaθ is :

Solution

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If $\sin 2\theta = \cos 40^\circ$ , then the smallest positive value of $\theta$ is :