Can you prove? Cosec^4(1+cos^2x)(1-cos^2x)-2cot^2x=1

Can you prove?
#Cosec^4x(1+cos^2x)(1-cos^2x)-2cot^2x=1#.

Can you prove?
#Cosec^4x(1+cos^2x)(1-cos^2x)-2cot^2x=1#.

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Feb 2, 2018

Answer:

Please refer to a Proof in the Explanation.

Explanation:

#color(red)(csc^4x)(1+cos^2x)color(red)((1-cos^2x))-2cot^2x#,

#=color(red)(csc^4x)(1+cos^2x)color(red)(sin^2x)-2cot^2x#,

#=color(red)(csc^2x)(1+cos^2x)-2cot^2x#,

#=color(red)(csc^2x)+csc^2xcos^2x-2cot^2x#,

#=color(red)(1+cot^2x)+color(green)(1/sin^2x*cos^2x)-2cot^2x#,

#=1+cancel(cot^2x+color(green)(cot^2x)-2cot^2x)#,

#=1#.

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