How to simplify 2 sin x csc 2x?

2 Answers
Øko
Mar 1, 2018

#2sin(x)csc(2x)=sec(x)#

Explanation:

We want to simplify

#2sin(x)csc(2x)#

Use the identity

  • #sin(2x)=2sin(x)cos(x)#

Thus

#2sin(x)csc(2x)=(2sin(x))/(sin(2x))=(2sin(x))/(2sin(x)cos(x))=sec(x)#

Jim G.
Mar 1, 2018

#secx#

Explanation:

#"using the "color(blue)"trigonometric identities"#

#•color(white)(x)secx=1/cosx" and "cscx=1/sinx#

#•color(white)(x)sin2x=2sinxcosx#

#rArr2sinx xx1/(sin2x)#

#=cancel(2sinx)xx1/(cancel(2sinx)cosx)#

#=1/cosx=secx#

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