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Prove that cos 570° sin 510° + sin (−330°) cos (−390°) = 0

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Question

Prove that cos 570° sin 510° + sin (−330°) cos (−390°) = 0

Sum

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Solution

LHS = cos(570°) sin(510°) + sin(−330°) cos(−390°)

= cos(570°) sin(510°) + [−sin(330°)]cos(390°)

= 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

= RHS

Hence proved .

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Trigonometric Equations

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Q 2.5 Q 2.4 Q 2.6

Chapter 5: Trigonometric Functions - Exercise 5.3 [Page 39]

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R.D. Sharma Mathematics [English] Class 11

Chapter 5 Trigonometric Functions
Exercise 5.3 | Q 2.5 | Page 39

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