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Prove the following: cos(3π4+x)-cos(3π4-x)=-2sinx

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प्रश्न

Prove the following:

`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`

योग
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उत्तर

L.H.S. = cos `((3x)/4 + x) - cos ( (3x) /4 - x)`

= - 2sin `[((3x)/4 + x) /2+ ( (3x) /4 - x)/2] sin [((3pi)/4)/2- ((3pi)/4-x)/2]` 

[cos (a + b) - cos (a - b) = - 2sin `((a +b)/2) sin  ((a + b )/2)`

= - 2sin `((3pi)/4) sin x = - 2 (pi - pi/4) sin x`

= - 2 x `1/sqrt2 sin x = - sqrt2 sin x` = R.H.S.

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अध्याय 3: Trigonometric Functions - EXERCISE 3.3 [पृष्ठ ६७]

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एनसीईआरटी Mathematics [English] Class 11
अध्याय 3 Trigonometric Functions
EXERCISE 3.3 | Q 11. | पृष्ठ ६७

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