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If sec 4x = csc (x - 20), where 4x is an acute angle, then find the value of x.  (All angles are in degrees.)

 Jan 11, 2020
 #1
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sec  and csc  are  co-functions

 

Specificallly

 

sec ( A)  =   csc (90 - A)

 

Note that

 

(A)  +  (90 -A)  = 90

 

So....this must mean that

 

(4x)  + (x - 20)   = 90

 

5x - 20  = 90   add 20 to  both  sides

 

5x = 110        divide both sides by 5

 

x = 22°

 

 

cool cool cool

 Jan 11, 2020

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