Prove the following identity algebraically?

I know that the LHS can be expanded to 2sintcost. I'm not sure how to solve this problementer image source here

1 Answer
Jim G.
Nov 5, 2017

#"see explanation"#

Explanation:

#"left hand side "=sin2t=2sintcost"#

#"right hand side"#

#=(2tant)/(1+tan^2t)#

#•color(white)(x)1+tan^2t=sec^2tlarrcolor(blue)"Pythagorean identity"#

#=(2tant)/(sec^2t)#

#•color(white)(x)sect=1/cost" and "tant=sint/cost#

#=(2tant)/(1/cos^2t)=2xxsint/costxxcos^2t=2sintcost#

#rArr"LHS "=" RHS"rArr"proved"#

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