Prove the identity. \frac{\sin(2x)}{\sin(x)}-\frac{\cos(2x)}{\cos(x)}=\sec(x)

jernplate8

jernplate8

Answered question

2021-09-11

Prove the identity
sin(2x)sin(x)cos(2x)cos(x)=sec(x)

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-09-12Added 117 answers

Solution:
sin(2x)sin(x)cos(2x)cos(x)=sec(x)
sin2x=2sinxcosx
cos22x=cos2xsin2x
=2sinxcosxsinxcos2xsin2xcosx
=2cosx(cos2xsin2x)cosx
Taking LCH
=2cos2xcos2x+sin2xcosx
=cos2x+sin2xcosx
sin2x+cos2x=1
1cosx=secx
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-10Added 2605 answers

Answer is given below (on video)

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