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...
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