Question

evaluate sec 41 degree sin 49 degree +cos 49 degree cosec 41 degree-2/root 3 tan 20 degree tan 60 degree tan 70 degree-3(cos 2 45 degree -sin2 90 degree

Answer 1

Step-by-step explanation:

=sec 41°× sin 49° + cos 49° cosec 41° -2/root 3 tan 20° tan 60° tan 70° -3(cos 2 45 - sin2 90°)

= Cosec (90-41)× Sin 49°+ Cos 49°× Sec (90-41)-(2/root 3)× Tan 20°× Tan 60°× Cot (90-70) - 3(1/2-1)

= (Cosec 49°×Sin 49°)+(Cos 49×Sec 49)-(2/root 3) [Tan 20°× Tan 60°×Cot 20°]-3(-1/2)

$(\frac{1}{sin \: 49} \times sin \: 49) + ( cos49 \times \frac{1}{cos \: 49}) - ( \frac{2}{ \sqrt{3} }) ( tan \: 20 \times \sqrt{3} \times \frac{1}{tan \: 20} ) - 3( \frac{1}{2} - 1) \\ = (1) + (1) - (2) + \frac{3}{2} \\ = 2 - 2 + \frac{3}{2} \\ = \frac{3}{2}$