Question Number 19860 by vivek last updated on 16/Aug/17
$$\mathrm{log}_{{e}} \sqrt{\frac{\mathrm{1}−{cox}}{\mathrm{1}+{cosx}}\:\:\boldsymbol{{differentiate}}\:\boldsymbol{{w}}.\boldsymbol{{r}}.\boldsymbol{{t}}\:\boldsymbol{{x}}} \\ $$
Answered by myintkhaing last updated on 17/Aug/17
$$\frac{\mathrm{d}}{\mathrm{dx}}\:\left(\mathrm{log}_{\mathrm{e}} \:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\right) \\ $$$$=\:\left(\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}}\right)\left(\frac{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}\left(−\mathrm{sin}\:\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }\right) \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}}\:=\:\mathrm{cosec}\:\mathrm{x} \\ $$
Commented by myintkhaing last updated on 16/Aug/17
$$\mathrm{we}\:\mathrm{use}\:\mathrm{in}\:\mathrm{our}\:\mathrm{country}\:... \\ $$$$\mathrm{sine}\:\rightarrow\:\mathrm{sin}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{cosecant}\rightarrow\mathrm{cosec} \\ $$$$\mathrm{cosine}\rightarrow\mathrm{cos}\:\:\:\:\:\:\:\:\:\:\mathrm{secant}\rightarrow\mathrm{sec} \\ $$$$\mathrm{tangent}\rightarrow\mathrm{tan}\:\:\:\:\:\mathrm{cotangent}\rightarrow\mathrm{cot} \\ $$
Commented by Joel577 last updated on 17/Aug/17
$$\frac{\mathrm{1}}{\mathrm{sin}\:{x}}\:=\:\mathrm{cosec}\:{x} \\ $$
Commented by vivek last updated on 17/Aug/17
$${sir}\:{answer}\:{is}\:{cosec}\:{x} \\ $$