How to solve 3sinx + 3cosx = secx + cosecx for x? Thank you!

1 Answer
Sunayan S
Feb 18, 2018

See the answer below...

Explanation:

#=>3sinx+3cosx=secx+cscx#

#=>3sinx+3cosx=1/cosx+1/sinx#

#=>3sinx+3cosx=(sinx+cosx)/(sinx cdot cosx#

#=>(sinx+cosx)(3-1/(sinx cdot cosx))=0#

#=>(sinx+cosx)(3-2/(2 cdot sinx cdot cosx))=0#

#=>(sinx+cosx)(3-2/sin(2x))=0#

Either,

#(sinx+cosx)=0#

#=>sinx=-cosx#

#=>tanx=-1=tan(-pi/4)#

#color(red)(ul(bar(|color(green)(=>x=npi-pi/4)|#

Or,

#(3-2/sin(2x))=0#

#=>2/sin(2x)=3#

#=>sin2x=2/3=sinalpha#

#=>2x=npi+(-1)^nalpha#

#=>color(red)(ul(bar(|color(green)(x=(npi)/2+(-1)^n(alpha/2))|#

Hope it helps...
Thank you...

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