Question

cosec10+cosec50-cosec70=?

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);

= 6

bye :-)

Answer 2

Cosec 10 +  cosec 50 - cosec 70
= Cosec 10 + 1/sin 50 - 1/sin 70
= cosec 10 + [sin 70 - sin 50]/ [sin 50 sin 70]
= cosec 10 + [ 2 cos 60 sin 10 ] / [ sin 50 sin 70 ]
= 1/ sin10 + sin 10 / [sin 50 sin 70 ]
= [sin 50 sin 70 + sin² 10 ] / { [ cos 20 - cos 120]/2 * Sin 10 }
= [ cos 20 - cos 120 + 1 - cos 20 ] / { [ cos 20 - cos 120 ] * Sin 10 }
= [ 3/2 ] / [ sin 10 cos 20 + 1/2 sin 10]
= 3 / [ sin 30 - sin 10 + sin 10 ]
= 3 / [ 1/2  ]
= 6