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Question Number 95524 by Abdulrahman last updated on 25/May/20

(1/(sin10))−((√3)/(cos10))=?

$$\frac{\mathrm{1}}{\mathrm{sin10}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{cos10}}=? \\ $$

Commented by PRITHWISH SEN 2 last updated on 25/May/20

((cos 10−(√3)sin 10)/(sin 10cos 10)) = 4((((1/2)cos 10−((√3)/2)sin 10))/(2sin 10cos 10)) =4.((sin 30.cos 10−cos 30.sin 10)/(sin 20)) =4.((sin (30−10))/(sin 20)) ((4.sin 20)/(sin 20)) = 4

$$\frac{\mathrm{cos}\:\mathrm{10}−\sqrt{\mathrm{3}}\mathrm{sin}\:\mathrm{10}}{\mathrm{sin}\:\mathrm{10cos}\:\mathrm{10}}\:=\:\mathrm{4}\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{10}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{sin}\:\mathrm{10}\right)}{\mathrm{2sin}\:\mathrm{10cos}\:\mathrm{10}} \\ $$$$=\mathrm{4}.\frac{\mathrm{sin}\:\mathrm{30}.\mathrm{cos}\:\mathrm{10}−\mathrm{cos}\:\mathrm{30}.\mathrm{sin}\:\mathrm{10}}{\mathrm{sin}\:\mathrm{20}}\:=\mathrm{4}.\frac{\mathrm{sin}\:\left(\mathrm{30}−\mathrm{10}\right)}{\mathrm{sin}\:\mathrm{20}} \\ $$$$\frac{\mathrm{4}.\mathrm{sin}\:\mathrm{20}}{\mathrm{sin}\:\mathrm{20}}\:=\:\mathrm{4} \\ $$

Commented by Abdulrahman last updated on 25/May/20

thanks but the second step?

$$\mathrm{thanks}\: \\ $$$$\mathrm{but}\:\mathrm{the}\:\mathrm{second}\:\mathrm{step}? \\ $$$$ \\ $$

Commented by Abdulrahman last updated on 25/May/20

bundle of thanks

$$\mathrm{bundle}\:\mathrm{of}\:\mathrm{thanks} \\ $$

Commented by Tony Lin last updated on 25/May/20

just change into (1/2)(((sin30)/(sin10))−((cos30)/(cos10))) and do addition formula of trigometry

$${just}\:{change}\:{into}\:\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{{sin}\mathrm{30}}{{sin}\mathrm{10}}−\frac{{cos}\mathrm{30}}{{cos}\mathrm{10}}\right) \\ $$$${and}\:{do}\:{addition}\:{formula}\:{of}\:{trigometry} \\ $$

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