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Show that cosec10+cosec50-cosec70=6. How do you solve this?

Harnoor , 7 Years ago
Grade 11
anser 1 Answers
Arun
cosec 10 + cosec 50 - cosec 70;
= (1/sin 10) + (1/sin 50) - (1/ sin 70);
= (sin 70 sin 50 + sin 70 sin 10 - sin 50 sin 10)/(sin 70 sin 50 sin 10);
= ((-1/2)(cos 120 - cos 20 + cos 80 - cos 60 - cos 60 + cos 40))/((-1/2)(cos 120 - cos 20)(sin 10));
= ((-1/2) - cos 20 + cos 80 - (1/2) - (1/2) + cos 40)/(((-1/2) - cos 20)(sin 10));
= ((-3/2) + cos 80 + cos 40 - cos 20)/((-1/2) sin 10 - cos 20 sin 10));
= ((-3/2) + 2 cos 60 cos 20 - cos 20)/((-1/2) sin 10 - (1/2)(sin 30 - sin 10));
= ((-3/2) + cos 20 - cos 20)/((-1/2) sin 10 - (1/4) + (1/2) sin 10);
= (-3/2)/(-1/4);
= 6

Regards
Arun (asmIITians forum expert)
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Last Activity: 7 Years ago
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