Question

Prove that cos 510 degree cos 330 degree + sin 390 degree cos 120 degree - 1

Answer 1

Answer:

Step-by-step explanation:

) cos 510 = cos ( 360 + 150 )

= Cos 150

= Cos ( 180 - 30 )

= - cos 30°

2 ) cos 330° = cos ( 360 - 30 )

= Cos 30

3 ) sin 390 = sin( 360 + 30 )

= Sin 30

4 ) cos 120 = cos ( 90 + 30 )

= - sin 30°

Now ,

Cos 510 cos 330 + sin390 cos 120

= ( -cos 30°)(cos 30°)+(sin30°)(-sin30°)

= - cos² 30° - sin² 30°

= - ( cos² 30° + sin² 30° )

= -1

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)

= -1

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