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

Mathematics

1 answer:

Mrac [35]2 years ago

6 0

Answer:

The bottom one ....see below

Step-by-step explanation:

Using reference angle of pi/8 and half angle trig identity:

cos ( angle/2) = -sqrt (1 + cos (angle) /2)

cos ( pi/4 / 2) = - sqrt (1+ cos ( pi/4)/2)

<u> cos (pi/8)</u> = - sqrt (1 + sqrt (2) / 2)

= - sqrt (1 + sqrt 2) / sqrt 2 rationalize the denominator

= - sqrt ( sqrt 2 + 2) / 2

re arrange to

- sqrt ( 2 + sqrt2) / 2 the fourth answer

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