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$\cos \frac{\pi}{2^2} \cdot \cos \frac{\pi}{2^3} \cdot \dots \cdot \cos \frac{\pi}{2^{10}} \cdot \sin \frac{\pi}{2^{10}}$ ની કિંમત શોધો.

જો $\sin^3 x \sin 3x = \sum_{m=0}^n c_m \cos mx$ હોય,જ્યાં $c_0, c_1, c_2, \dots, c_n$ અચળાંકો છે અને $c_n \neq 0$,તો $n$ ની કિંમત શોધો.

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જો $90^\circ < A < 180^\circ$ અને $\sin A = \frac{4}{5}$ હોય,તો $\tan \frac{A}{2}$ ની કિંમત શોધો.

જો $3 \sin \theta = 2 \sin 3 \theta$ અને $0 < \theta < \pi$ હોય,તો $\sin \theta =$

સાબિત કરો કે $\sin 2x + 2 \sin 4x + \sin 6x = 4 \cos^2 x \sin 4x$.

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