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cos(sin^(-1)(-(1)/(2)))+tan^(-1)(cos(\pi ))

 Aug 20, 2021
 #1
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+1

cos pi = -1

tan-1 (-1) =  135 degrees

 

 

sin-1/2  (-1/2) =   -30      or     210   degrees       

 

The , remember this identity:   cos(α+β)=cosαcosβ−sinαsinβ       and apply it to the following:

 

cos ( -30   + 135)                         cos ( 210 + 135)

 Aug 20, 2021
 #2
avatar+114536 
+1

cos(sin^(-1)(-(1)/(2)))+tan^(-1)(cos(\pi ))

 

\(cos(asin\frac{-1}{2})+atan(cos(\pi ))\\ =cos(2\pi-\frac{\pi}{6})+atan(-1)\\ =cos(\frac{\pi}{6})+\frac{-\pi}{4}\\ =\frac{\sqrt3}{2}-\frac{\pi}{4}\\ =\frac{2\sqrt3-\pi}{4}\\\)

 Aug 20, 2021

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