How do you prove: $[(sinx/cosx) +(cosx/sinx)] = sinx^2+cosx^2$ ?

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Answer 1 · 2016-03-26T20:53:26

The given identity is false.

Consider $x = pi/4$

$sin(pi/4)/cos(pi/4)+cos(pi/4)/sin(pi/4) = (sqrt(2)/2)/(sqrt(2)/2)+(sqrt(2)/2)/(sqrt(2)/2) = 1+1=2$

but

$sin((pi/4)^2)+cos((pi/4)^2) = sin(pi^2/16)+cos(pi^2/16) ~~1.394$

How do you prove: [(sinx/cosx) +(cosx/sinx)] = sinx^2+cosx^2 [(sinx/cosx) +(cosx/sinx)] = sinx^2+cosx^2?