Question

5. Prove that
cos 570° sin 510° + sin (-330°) cos (- 390°) = 0.​

Answer 1

Now cos(540+30) x sin (540-30) = -cos30 x sin30 = -sin30cos30
Also, sin(-330) cos(-390) = -sin330 x cos390 = -sin(360-30) cos(360+30)= - (-sin30) x cos30 = sin30cos30
Sum = sin30cos30 - sin30cos30 = 0

Answer 2

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LHS =cos (570)sin (510) + sin (- 330)cos (- 390)

= cos (570) sin (510) + [ – sin (330) ]cos (390) [ because sin( – x ) = – sin x and cos( – x ) = cos x ]

= cos (570)sin(510) – sin (330)

= cos (90 * 6 + 30) sin (90 * 5 + 60) – sin (90 * 3 + 60) cos (90 * 4 + 30)

= – cos (30) cos (60) – [ – cos (60) ] cos (30)

= – cos (30) cos (60) + cos (30) sin (60)

= 0

Hope it's Helpful.....:)