Write the given expression as an algebraic expression in x.co cos-(*)

Consider the given expression, cos12cos-1x=coscos-1x2 As we know,…

Answered: rite the given express as an aigebraic…

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter5: Identities And Formulas

Section5.5: Additional Identities

Problem 21PS

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Write the given expression as an algebraic expression in x.
co cos-(*)

Expert Solution

Step 1

Consider the given expression,

$\cos (\frac{1}{2} \cos^{- 1} (x)) = \cos (\frac{\cos^{- 1} (x)}{2})$

As we know,

$\begin{array}{rcl} \cos (θ) & = & 2 \cos^{2} (\frac{θ}{2}) - 1 \\ \cos (θ) + 1 & = & 2 \cos^{2} (\frac{θ}{2}) \\ \cos^{2} (\frac{θ}{2}) & = & \frac{1 + \cos (θ)}{2} \\ \cos (\frac{θ}{2}) & = & \pm \sqrt{\frac{1 + \cos (θ)}{2}} \end{array}$

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