Question

Help me solve this problem.

Answer 1

Things to know :

1) Componendo and Dividendo ,

If a/b = c/d
then by componendo and dividendo,
(a+b)/(a-b) = (c +d)/(c-d)

2) 2 sin (a) cos( b )= sin ( a + b) + sin (a-b)
sin ( a + b ) = sin a cos b + cos a sin b

sin (a-b)= sin a cos b -cos a sin b
cos (a + b ) = cos a cos b - sin a sin b
cos ( a - b) = cos a cos b + sin a sin b

and other similar identities .

3) sin ( 270°-a) = ( - ) cos a
sin (150°) = 1/2

For Calulation Process See Pic :
Final result:
Smaller angle = 30°





Hope, you understand my answer.