What is the exact value of cos(7pi/8)

The exact value of cos(7pi/8) is and this can be determined by using the trigonometric properties.

Given :

Expression  --

The following steps can be used to determine the exact value of the given expression:

Step 1 - Write the given expression.

Step 2 - Rewrite the above expression.

Step 3 - The above expression is reduced to:

   --- (1)

Step 4 - According to the trigonometric properties:

Step 5 - Substitute the value of x = /4 in the above expression.

Step 6 - Simplify the above expression.

Step 7 - Substitute the value of cos(/8) in the expression (1).

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cos () =

Decimal value: −0.9238795325...

Step-by-step explanation:

Write,

cos = cos = −cos

Now using half angle formula, cos(x) = 2 cos²() − 1, we can write cos = 2

cos²() − 1

This means + 1 = 2 cos²()

2 cos²() =

cos²() =

cos() =

Simplify,

= =

Hence,

cos () = −cos () =