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Question Number 83229 by peter frank last updated on 28/Feb/20

Commented by jagoll last updated on 28/Feb/20

$$\left(\mathrm{iii}\right)\frac{\cos 3\mathrm{A}-\cos 9\mathrm{A}+\cos \mathrm{A}-\cos 3\mathrm{A}}{\sin 9\mathrm{A}-\sin 3\mathrm{A}+\sin 3\mathrm{A}-\sin \mathrm{A}}$$$$=\frac{\cos \mathrm{A}-\cos 9\mathrm{A}}{\sin 9\mathrm{A}-\sin \mathrm{A}}=\frac{2\sin 5\mathrm{Asin}4\mathrm{A}}{2\cos 5\mathrm{Asin}4\mathrm{A}}$$$$=\tan 5\mathrm{A}$$

Commented by peter frank last updated on 28/Feb/20

$$thankyousir.$$$$isitpossibletofind$$$$generalvalueinb\left(i\right)?$$

Commented by jagoll last updated on 28/Feb/20

$$\left(\mathrm{i}\right)\cos \mathrm{px}+\cos \mathrm{qx}=0$$$$2\cos \left(\frac{\mathrm{p}+\mathrm{q}}{2}\right)\mathrm{x}\cos \left(\frac{\mathrm{p}-\mathrm{q}}{2}\right)\mathrm{x}=0$$$$\Rightarrow \cos \left(\frac{\mathrm{p}+\mathrm{q}}{2}\right)\mathrm{x}=\cos \frac{\pi }{2}$$$$\left(\frac{\mathrm{p}+\mathrm{q}}{2}\right)\mathrm{x}=\pm \frac{\pi }{2}+2\mathrm{k}\pi \Rightarrow \mathrm{x}=\frac{\pm \pi +4\mathrm{k}\pi }{\mathrm{p}+\mathrm{q}}$$$$\Rightarrow \mathrm{similarly}\cos \left(\frac{\mathrm{p}-\mathrm{q}}{2}\right)\mathrm{x}=\pm \frac{\pi }{2}+2\mathrm{k}\pi$$$$\mathrm{x}=\frac{\pm \pi +4\mathrm{k}\pi }{\mathrm{p}-\mathrm{q}}$$

Commented by peter frank last updated on 28/Feb/20

$$thankyou$$

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