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...

:-)