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Category: Integration

Question-163197

Question Number 163197 by abdullahhhhh last updated on 04/Jan/22 Commented by cortano1 last updated on 05/Jan/22 $$\mathrm{cos}\:\mathrm{5}{x}=\mathrm{cos}\:^{\mathrm{5}} {x}−\mathrm{10sin}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:^{\mathrm{3}} {x}+\mathrm{5sin}\:^{\mathrm{4}} {x}\:\mathrm{cos}\:{x} \\ $$$$\mathrm{sin}\:\mathrm{4}{x}=\mathrm{4sin}\:{x}\:\mathrm{cos}\:^{\mathrm{3}} {x}−\mathrm{4sin}\:^{\mathrm{3}} {x}\:\mathrm{cos}\:{x}…

prove-that-0-pi-4-sin-x-cos-x-1-sin-x-cos-x-dx-2-cot-1-2-

Question Number 163158 by mnjuly1970 last updated on 04/Jan/22 $$ \\ $$$$\:\:\:\:\:{prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\:{sin}\left({x}\right)+{cos}\left({x}\right)}{\:\sqrt{\mathrm{1}+{sin}\left({x}\right){cos}\left({x}\right)}}\:{dx}=\:\sqrt{\mathrm{2}}\:.{cot}^{\:−\mathrm{1}} \left(\sqrt{\mathrm{2}}\:\right) \\ $$$$\:\:\:−−−−− \\ $$ Answered by mahdipoor last…