Is following expression true?cos⁡570∘sin⁡510∘+sin⁡-330∘cos⁡-390∘=0

Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

Is following expression true?

$\cos (570^{\circ}) \sin (510^{\circ}) + \sin (- 330^{\circ}) \cos (- 390^{\circ}) = 0$

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The given expression is,

\cos (570^{\circ}) \sin (510^{\circ}) + \sin (- 330^{\circ}) \cos (- 390^{\circ}) = 0

Take left hand side

\cos (570^{\circ}) \sin (510^{\circ}) + \sin (- 330^{\circ}) \cos (- 390^{\circ})

As,

\sin (- x) = - \sin x

and

\cos (- x) = \cos x

. Thus, the above expression can be written as,

= \cos (570^{\circ}) \sin (510^{\circ}) - \sin (330^{\circ}) \cos (390^{\circ})

= co s (90^{\circ} \times 6 + 30^{\circ}) si n (90^{\circ} \times 6 - 30^{\circ}) - \sin (360^{\circ} - 30^{\circ}) \cos (360^{\circ} + 30^{\circ})

= - co s (30^{\circ}) si n (30^{\circ}) - \sin (30^{\circ}) \cos (30^{\circ})

= (- \frac{\sqrt{3}}{2}) \times (\frac{1}{2}) - (- \frac{1}{2}) \times (\frac{\sqrt{3}}{2})

= - \frac{\sqrt{3}}{4} + \frac{\sqrt{3}}{4}

= 0

Thus,

\cos (570^{\circ}) \sin (510^{\circ}) + \sin (- 330^{\circ}) \cos (- 390^{\circ}) = 0

Correct option is 1.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE