Maharashtra State BoardHSC Science (General) 11th
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Find values of : sin π8 - Mathematics and Statistics

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Sum

Prove the following:

`sin  pi^"c"/8 = 1/2sqrt(2 - sqrt(2))`

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Solution

We know that cos `pi/4 = 1/sqrt(2)`

Also `pi/8`  lies in the first quadrant, hence sin `pi/8` is positive.

Now, cos 2θ = 1 − 2sin2 θ

By putting θ = `pi/8`, we get,

`cos  pi/4 = 1 - 2sin^2  pi/8`

∴ `2sin^2  pi/8 = 1 - cos  pi/4`

= `1 - 1/sqrt(2)`

= `(sqrt2-1)/sqrt2`

∴ `sin^2  pi/8 = (sqrt(2) - 1)/(2sqrt(2))`

= `(sqrt(2)(sqrt(2) - 1))/4`

= `(2 - sqrt(2))/4`

∴ `sin  pi/8 = 1/2 sqrt(2-sqrt2)` ......`[∵ sin  pi/8  "is positive"]`

Concept: Trigonometric Functions of Double Angles
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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. (26) | Page 58
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