Question #06769

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Answer 1 · 2017-10-15T15:16:54

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

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

$=sin60cos30+cos60sin30$

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

Answer 2 · 2017-10-15T15:46:23

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

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.