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Let x be an acute angle such that \tan x + \sec x = 0. Find $\cos x$.

 May 30, 2024
 #1
avatar+129487 
+1

tanx + sec x =  0

 

sin x / cos x  +  1 / cos x =   0

 

sin x / cos x =   -1  / cos x           square both sides

 

sin^2 x / cos^2x  = 1 / cos^2 x

 

[ 1 - cos ^2 x ]  / cos ^2 x  = 1/ cos^2 x

 

1/ cos ^2 x  -  1  = 1/ cos^2 x

 

-1  =  0         →  no solution

 

cool cool cool

 May 30, 2024

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