1
MHT CET 2021 23th September Morning Shift
+2
-0

If $$3 \sin \theta=2 \sin 3 \theta$$ and $$0< \theta<\pi$$, then $$\sin \theta=$$

A
$$\frac{\sqrt{2}}{\sqrt{5}}$$
B
$$\frac{\sqrt{3}}{2 \sqrt{2}}$$
C
$$\frac{\sqrt{2}}{3}$$
D
$$\frac{\sqrt{3}}{\sqrt{5}}$$
2
MHT CET 2021 21th September Evening Shift
+2
-0

The number of solutions of cos2$$\theta$$ = sin$$\theta$$ in (0, 2$$\pi$$) are

A
3
B
2
C
4
D
1
3
MHT CET 2021 21th September Evening Shift
+2
-0

If $$\theta+\phi=\alpha$$ and $$\tan \theta=k \tan \phi($$ where $$K>1)$$, then the value of $$\sin (\theta-\phi)$$ is

A
$$\mathrm{k} \tan \phi$$
B
$$\sin \alpha$$
C
$$\left(\frac{\mathrm{k}-1}{\mathrm{k}+1}\right) \sin \alpha$$
D
$$\mathrm{k} \cos \phi$$
4
MHT CET 2021 21th September Morning Shift
+2
-0

$$2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)$$, then $$\tan \theta=$$

A
$$\frac{-1}{\sqrt{3}}$$
B
$$-\sqrt{3}$$
C
$$\sqrt{3}$$
D
$$\frac{1}{\sqrt{3}}$$
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