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Prove the following: cos2 2x – cos2 6x = sin 4x sin 8x

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Question

Prove the following:

cos2 2x – cos2 6x = sin 4x sin 8x

Sum
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Solution

cos2 2x – cos2 6x = (cos2x + cos6x) (cos 2x - cos 6x)

= `2cos  ((2x + 6x)/2) cos ((2x - 6 x) /2) - 2sin ((2x - 6x)/2) sin ((2x + 6x)/2)`

= (2cos 4x cos2x) (2sin 4x sin 2x)

= (2sin 2x cos2x)(2sin 4x cos4x) = sin 4x sin 8x

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Chapter 3: Trigonometric Functions - EXERCISE 3.3 [Page 67]

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NCERT Mathematics [English] Class 11
Chapter 3 Trigonometric Functions
EXERCISE 3.3 | Q 13. | Page 67

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