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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 Number 120621 by TANMAY PANACEA last updated on 01/Nov/20 $${Trigonometry} \\ $$$${selective}\:{questions} \\ $$ Commented by TANMAY PANACEA last updated on 01/Nov/20 Commented by…
Question Number 120614 by TANMAY PANACEA last updated on 01/Nov/20 $${Trigonometry}\: \\ $$ Commented by TANMAY PANACEA last updated on 01/Nov/20 Commented by TANMAY PANACEA…
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…
Question Number 186125 by Mingma last updated on 01/Feb/23 Answered by som(math1967) last updated on 01/Feb/23 $${let}\:\mathrm{2}^{{sin}\alpha} =\mathrm{3}^{{sin}\beta} =\mathrm{5}^{{sin}\theta} ={k} \\ $$$$\Rightarrow{k}^{\frac{\mathrm{1}}{{sin}\alpha}} =\mathrm{2}\Rightarrow{k}^{{cosec}\alpha} =\mathrm{2} \\…
Question Number 186126 by Mingma last updated on 01/Feb/23 Commented by Frix last updated on 01/Feb/23 $$\mathrm{tan}\:\mathrm{2}\alpha\:=\frac{\mathrm{2tan}\:\alpha}{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \:\alpha}\:\Rightarrow \\ $$$$\mathrm{tan}\:\mathrm{4}\alpha\:=\mathrm{tan}\:\left(\mathrm{2}×\left(\mathrm{2}\alpha\right)\right)\:=\frac{\mathrm{4}\left(\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \:\alpha\right)\mathrm{tan}\:\alpha}{\mathrm{1}−\mathrm{6tan}^{\mathrm{2}} \:\alpha\:+\mathrm{tan}^{\mathrm{4}} \:\alpha} \\ $$…