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Category: Trigonometry

show-that-lim-x-0-sinx-x-1-

Question Number 121050 by mathocean1 last updated on 05/Nov/20 $$\mathrm{show}\:\mathrm{that}\: \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{0}\:} {\mathrm{lim}}\:\frac{\mathrm{sinx}}{\mathrm{x}}=\mathrm{1} \\ $$ Answered by 675480065 last updated on 05/Nov/20 $$\mathrm{as}\:\mathrm{x}\rightarrow\mathrm{0},\:\mathrm{sinx}\rightarrow\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}!}+\mathrm{0}\left(\mathrm{x}^{\mathrm{3}} \right)\right)…

prove-the-following-identities-a-sin-1-cos-2-tan-b-1-cos-2-sin-sin-2-cos-tan-c-cos-x-y-sin-x-y-cos-2ycos-2x-1-cos-x-y-sin-y-x-

Question Number 55141 by 0201011563081 last updated on 18/Feb/19 $${prove}\:{the}\:{following}\:{identities} \\ $$$$ \\ $$$${a}.\frac{\mathrm{sin}\:\theta}{\mathrm{1}+\mathrm{cos}\:\mathrm{2}\theta}=\mathrm{tan}\:\theta \\ $$$${b}.\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{2}\theta−\mathrm{sin}\:\theta}{\mathrm{sin}\:\mathrm{2}\theta−\mathrm{cos}\:\theta}=\mathrm{tan}\:\theta \\ $$$${c}.\frac{\mathrm{cos}\:\left({x}+{y}\right)+\mathrm{sin}\:\left({x}−{y}\right)}{\mathrm{cos}\:\mathrm{2}{y}\mathrm{cos}\:\mathrm{2}{x}}=\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}+{y}\right)\mathrm{sin}\:\left({y}−{x}\right)} \\ $$ Commented by math1967 last updated…

Question-186144

Question Number 186144 by Rupesh123 last updated on 01/Feb/23 Commented by mr W last updated on 01/Feb/23 $${if}\:{the}\:{age}\:{of}\:{your}\:{father}\:{is}\:\mathrm{3}\:{times}\:{of} \\ $$$${your}\:{age},\:\:{then}\:{how}\:{far}\:{is}\:{your}\:{school}\: \\ $$$${away}\:{from}\:{your}\:{home}? \\ $$ Commented…