+0  
 
+1
72
3
avatar+79 

 

Not sure how to do these.. Would be grateful if steps are shown and x values are in radians..

UpTheChels  Nov 23, 2017
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3+0 Answers

 #1
avatar+79846 
+2

 

8 tan (x)  + 11  = 19     subtract 11 from  both sides

 

8 tan (x)  =  8      divide both sides by  8

 

tan ( x)  = 1

 

And this is true when x  =  pi/4     and   x  = 5pi/4   in  the requested interval

 

 

cool cool cool

CPhill  Nov 23, 2017
 #2
avatar+79846 
+2

sec^2 (x)  = 2 tan^2 (x)

 

Note that   tan^2(x)  + 1  =  sec^2 (x)....so we can write

 

tan^2(x)  +  1  =  2tan^2(x)      rearrange as

 

tan^2(x)  = 1   subtract 1 from both sides

 

tan^2 (x)  - 1  =  0     factor

 

(tan (x) + 1) ( tan (x)  - 1)  = 0

 

Set each factor to ) and solve

 

tan (x)  +  1  =  0                                       tan (x) - 1  = 0

 

tan (x)  = -1                                               tan (x)  =  1

 

And this is true at                                     And this is true at 

 

3pi/4  ± n*pi                                             pi/4  ± n*pi

 

Where n is an integer

 

cool cool cool

CPhill  Nov 23, 2017
edited by CPhill  Nov 23, 2017
edited by CPhill  Nov 23, 2017
 #3
avatar+79846 
+1

sec^2(x)  + sec^2(x)  - 1  = 3    subtract 1 from both sides

 

2sec^2(x)  = 2     divide both sides by 2

 

sec^2(x)   = 1   subtract 1 from both sides

 

sec^2(x)  - 1  = 0     factor

 

( sec (x)  - 1)  (sec (x)  + 1 )   = 0

 

Set  each factor to 0  and solve

 

sec(x)  - 1  = 0                              sec(x)  +  1  = 0

 

sec(x)  = 1                                    sec(x)  = -1

 

And this is true at                        And this is true at

 

0  ± n*2pi                                       pi ± n*2pi

 

Where n is an integer

 

 

cool cool cool

CPhill  Nov 23, 2017
edited by CPhill  Nov 23, 2017

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