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...
:-)
