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Category: Trigonometry

nice-calculus-in-AB-C-cos-A-cos-B-cos-C-1-9-find-the-value-of-cos-2-A-cos-2-B-cos-2-C-

Question Number 136094 by mnjuly1970 last updated on 19/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:….\:{nice}\:\:\:\:{calculus}…. \\ $$$$\:\:\:\:{in}\:{A}\overset{\Delta} {{B}C}\:::\:{cos}\left({A}\right){cos}\left({B}\right){cos}\left({C}\right)=\frac{\mathrm{1}}{\mathrm{9}} \\ $$$$\:\:\:{find}\:\:{the}\:{value}\:{of}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{cos}^{\mathrm{2}} \left({A}\right)+{cos}^{\mathrm{2}} \left({B}\right)+{cos}^{\mathrm{2}} \left({C}\right)=? \\ $$ Commented by MJS_new…

A-piece-of-plastic-strip-1-metre-long-is-bent-to-form-an-isosceles-triangle-with-95-as-measure-of-its-largest-angle-Find-the-length-of-the-sides-

Question Number 5008 by Rasheed Soomro last updated on 31/Mar/16 $$\mathrm{A}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{plastic}\:\mathrm{strip}\:\mathrm{1}\:\mathrm{metre}\:\mathrm{long} \\ $$$$\mathrm{is}\:\mathrm{bent}\:\mathrm{to}\:\mathrm{form}\:\mathrm{an}\:\mathrm{isosceles}\:\mathrm{triangle} \\ $$$$\mathrm{with}\:\mathrm{95}°\:\mathrm{as}\:\mathrm{measure}\:\mathrm{of}\:\mathrm{its}\:\mathrm{largest}\:\mathrm{angle}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}. \\ $$ Commented by prakash jain last updated…

cos-x-tan-x-sin-3-x-cos-3-x-

Question Number 136008 by liberty last updated on 17/Mar/21 $$\:\mathrm{cos}\:{x}\:\sqrt{\mathrm{tan}\:{x}}\:=\:\mathrm{sin}\:^{\mathrm{3}} {x}+\mathrm{cos}\:^{\mathrm{3}} {x} \\ $$ Answered by MJS_new last updated on 17/Mar/21 $${t}=\sqrt{\mathrm{tan}\:{x}}\:\wedge{t}\geqslant\mathrm{0} \\ $$$$\frac{{t}}{\left({t}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}}…

montrer-que-sinA-sinB-sinC-4cos-A-2-cos-B-2-cos-C-2-

Question Number 70394 by Cmr 237 last updated on 04/Oct/19 $$\mathrm{montrer}\:\mathrm{que} \\ $$$$\mathrm{sinA}+\mathrm{sinB}+\mathrm{sinC}=\mathrm{4cos}\frac{\mathrm{A}}{\mathrm{2}}\mathrm{cos}\frac{\mathrm{B}}{\mathrm{2}}\mathrm{cos}\frac{\mathrm{C}}{\mathrm{2}} \\ $$ Answered by $@ty@m123 last updated on 05/Oct/19 $${LHS}=\mathrm{2sin}\:\frac{{A}+{B}}{\mathrm{2}}\mathrm{cos}\:\frac{{A}−{B}}{\mathrm{2}}+\mathrm{sin}\:{C} \\ $$$$=\mathrm{2sin}\:\frac{\pi−{C}}{\mathrm{2}}\mathrm{cos}\:\frac{{A}−{B}}{\mathrm{2}}+\mathrm{sin}\:{C}…

Question-135868

Question Number 135868 by liberty last updated on 16/Mar/21 Answered by EDWIN88 last updated on 16/Mar/21 $$\mathrm{we}\:\mathrm{know}\:\mathrm{that}\:−\mathrm{1}\leqslant\mathrm{cos}\:\mathrm{x}\leqslant\mathrm{1}\:\mathrm{for}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{2}\pi\:;\:\mathrm{so}\:\mathrm{we}\:\mathrm{find}\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{−\mathrm{x}^{\mathrm{3}} −\mathrm{2x}^{\mathrm{2}} −\mathrm{5x}}{\mathrm{2}} \\ $$$$\mathrm{then}\:−\mathrm{2}\leqslant−\mathrm{x}^{\mathrm{3}} −\mathrm{2x}^{\mathrm{2}} −\mathrm{5x}\leqslant\mathrm{2}\:\mathrm{or}\:…

What-are-the-possible-value-of-cos-sin-if-sin-cos-1-2-

Question Number 135855 by liberty last updated on 16/Mar/21 $${What}\:{are}\:{the}\:{possible}\:{value}\:{of} \\ $$$$\mathrm{cos}\:\alpha×\mathrm{sin}\:\beta\:\:{if}\:\mathrm{sin}\:\alpha×\mathrm{cos}\:\beta=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by EDWIN88 last updated on 16/Mar/21 $$\mathrm{We}\:\mathrm{have}\:−\mathrm{1}\leqslant\mathrm{sin}\:\left(\alpha+\beta\right)\leqslant\mathrm{1}\:\mathrm{and}\:−\mathrm{1}\leqslant\mathrm{sin}\:\left(\alpha−\beta\right)\leqslant\mathrm{1} \\ $$$$\mathrm{now}\:\mathrm{from}\:−\mathrm{1}\leqslant\mathrm{sin}\:\left(\alpha+\beta\right)\leqslant\mathrm{1}\:\mathrm{we}\:\mathrm{get}\: \\…

Find-the-minimum-value-of-sin-x-cos-x-tan-x-cot-x-sec-x-csc-x-for-real-numbers-x-

Question Number 135792 by benjo_mathlover last updated on 16/Mar/21 $${Find}\:{the}\:{minimum}\:{value} \\ $$$${of}\:\mid\mathrm{sin}\:{x}+\mathrm{cos}\:{x}+\mathrm{tan}\:{x}+\mathrm{cot}\:{x}+\mathrm{sec}\:{x}+\mathrm{csc}\:{x}\mid\: \\ $$$${for}\:{real}\:{numbers}\:{x}. \\ $$ Answered by MJS_new last updated on 16/Mar/21 $${x}={t}+\frac{\mathrm{5}\pi}{\mathrm{4}}\:\mathrm{leads}\:\mathrm{to} \\…