Solve for #x#: #2tan^-1(cosx)=tan^-1(2cscx)#?

1 Answer
May 6, 2018

See the answer below...

Explanation:

Necessary formula:-

  • #color(red)(ul(bar(|color(green)(2tan^-1x=tan^-1((2x)/(1-x^2)))|#

  • #color(red)(ul(bar(|color(blue)(sin^2x+cos^2x=1)|#

  • Complementary angle formulae...

#2tan^-1(cosx)=tan^-1(2cscx)#

#=>tan^-1((2cosx)/(1-cos^2x))=tan^-1(2cscx)#

#=>(2cosx)/(1-cos^2x)=2cscx#

#=>(2cosx)/sin^2x=2/sinx#

#=>cosx/sinx=1#

#=>cotx=1#

#=>cotx=pi/4#

#=>x=npi+pi/4" "(n in I)#

Hope it helps...

Thank you...

:-)