Question

the value of cosec10 + cosec 50 - cos 70

Answer 1

Hello,

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);

HOPE THIS WILL HELP YOU

= 6