Question

Find the principal solution of cotx = -√3

=============================================

Prove that tan56 = $\frac{cos11+sin11}{cos11-sin11}$

Answer 1

i hope u will satisfy with my ans 

Answer 2

  cos(a-b) = cos(a)cos(b) + sin(a) sin(b) 
cos 11 = cos (56-45) = cos 56 cos 45 + sin 56 sin 45 = cos 56 / √2 + sin 56/√2 
sin(a-b) = sin(a) cos(b) - cos(a) sin(b) 
sin 11 = sin(56-45) = sin 56 cos 45 - cos 56 sin 45 = sin 56 /√2 - cos 56 / √2 

cos 11 + sin 11 = cos 56 / √2 + sin 56/√2 + sin 56 /√2 - cos 56 / √2 
cos 11 + sin 11 = (2/√2) sin 56 
cos 11 - sin 11 = cos 56 / √2 + sin 56/√2 - sin 56 /√2 + cos 56 / √2 
cos 11 - sin 11 = (2/√2) cos 56 

(cos 11 + sin 11)/(cos 11 - sin 11) = (2/√2) sin 56 / (2/√2) cos 56 
= tan 56