+0  
 
0
66
2
avatar

If sec(x) + tan(x) = 5/2, then find tan(x).

 Aug 8, 2020
 #1
avatar
0

I believe that the answer is 1.05.

 Aug 8, 2020
 #2
avatar+21953 
0

To expand upon Guest's answer:

 

sec(x) + tan(x)  =  5/2     --->     1 / cos(x)  +  sin(x) / cos(x)  =  5/2

 

Multiplying each side by  2·cos(x)   --->         2( 1 + sin(x) )  =  5( cos(x) )

Squaring both sides:                      4( 1 + 2sin(x) + sin2(x) )  =  25cos2(x)

Since  cos2(x) = 1 - sin2(x):                4 + 8sin(x) + 4sin2(x)  =  25 - 25sin2(x)

Rewriting:                                        29sin2(x) + 8sin(x) - 21  =  0

Quadratic formula:                                                      sin(x)  =  [ -8 +/- sqrt(2500) ] / 58

Choosing the positive answer:                                    sin(x)  =  42/58

 

Taking the opposite side as 42 and the hypotenuse as 58, 

by the Pythagorean formula, the adjacent side will be 40,

which means that the value of tangent is 42 / 40  =  1.05.

 Aug 8, 2020

33 Online Users

avatar
avatar