Question #06769

2 Answers
Oct 15, 2017

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

=sin(490+60)cos(49030)+cos(490+60)sin(490+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(θ)=cosθandsin(θ)=sinθ]

sin60cos30cos(4.9060)sin(4.9030)

sin60cos30cos60(sin30)

sin60cos30+cos60sin30

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

sin90

1 = R.H.S.