Question #06769

2 Answers
Oct 15, 2017

#LHS=sin(420)cos(330)+cos(300)sin(-330)#

#=sin(4*90+60)cos(4*90-30)+cos(-4*90+60)sin(-4*90+30)#

#=sin60cos30+cos60sin30#

#=sin(60+30)=sin90=1=RHS#

Oct 15, 2017

Proved sin(420) cos(390) + cos(-300) sin(-330) = 1

Explanation:

We have to prove sin(420) cos(390) + cos(-300) sin(-330) = 1

Left Hand Side (L.H.S.)
#Sin ( 4. 90+60). cos ( 4. 90 + 30) + cos(300) [- sin (330)]#
[ As #cos (-theta) = cos theta and sin(-theta)= - sin theta]#

#rArr sin 60 cos 30 - cos(4. 90 - 60) sin(4. 90 -30)#

#rArr sin 60 cos 30 - cos 60 ( - sin 30)#

#rArr sin 60 cos 30 + cos 60 sin 30#

#rArr sin (60+30)# [ As sin(a+b) = sin a cos b + cos a sin b]

#rArr sin 90#

#rArr 1# = R.H.S.