Maharashtra State BoardHSC Science (General) 11th
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Prove the following: cos(π4+x)+cos(π4-x)=2cosx - Mathematics and Statistics

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Sum

Prove the following:

`cos(pi/4 + x) + cos(pi/4 - x) = sqrt(2)cosx`

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Solution

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

= `2cos([pi/4 + x + pi/4 - x)/2)cos((pi/4 + x - (pi/4 - x))/2)`

= `2cos  pi/4 cosx`

= `2(1/sqrt(2))cosx`

= `sqrt(2)cosx`

= R.H.S.

Concept: Trigonometric Functions of Triple Angle
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Trigonometry - 2
Miscellaneous Exercise 3 | Q II. (6) | Page 57
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