How do you solve this? 2tanx = sin2x

1 Answer
MattyMatty
Mar 3, 2018

#x = k pi" , "k" any integer"#

Explanation:

#"Use"#
#color(red) (tan(x) = sin(x)/cos(x))#
#"And"#
#color(red) (sin(2x) = 2 sin(x) cos(x))#
#=> 2 tan(x) = 2 sin(x)/cos(x) = 2 sin(x) cos(x)#
#"Now divide both sides by "sin(x)!="0" !"#
#=> 1/cos(x) = cos(x)#
#=> 1 = cos^2(x)#
#=> cos(x) = pm 1#
#=> x = k pi" with "k" any integer"#
#"We still have to check the case "sin(x)=0" : "#
#"This case yields the same solution "x= k pi"."#
#"So we conclude : "#

#x = k pi" , "k" any integer"#

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