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Author: Tinku Tara

0-sin-px-x-dx-p-R-

Question Number 128314 by 676597498 last updated on 06/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\mathrm{px}\right)}{\:\sqrt{\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\forall\mathrm{p}\in\mathbb{R} \\ $$ Answered by Dwaipayan Shikari last updated on 06/Jan/21 $$\int_{\mathrm{0}}…

if-cos-cosA-cosB-1-cosA-cosB-prove-that-Tan-2-Tan-A-2-Cot-B-2-

Question Number 62761 by lalitchand last updated on 25/Jun/19 $$\mathrm{if}\:\mathrm{cos}\theta=\frac{\mathrm{cosA}.\mathrm{cosB}}{\mathrm{1}−\mathrm{cosA}.\mathrm{cosB}}\:\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{Tan}\frac{\theta}{\mathrm{2}}=\mathrm{Tan}\frac{\mathrm{A}}{\mathrm{2}}.\mathrm{Cot}\frac{\mathrm{B}}{\mathrm{2}} \\ $$ Commented by Prithwish sen last updated on 25/Jun/19 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{cos}\theta\:=\:\frac{\mathrm{cosA}−\mathrm{cosB}}{\mathrm{1}−\mathrm{cosAcosB}} \\ $$$$\frac{\mathrm{1}−\mathrm{cos}\theta}{\mathrm{1}+\mathrm{cos}\theta}\:=\:\frac{\mathrm{1}−\mathrm{cosA}+\mathrm{cosB}−\mathrm{cosAcosB}}{\mathrm{1}+\mathrm{cosA}−\mathrm{cosB}−\mathrm{cosAcosB}}…