Pruebalo $(sinx-cosx)^2=1-1/csc^2x$ ?

Question

1226 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-24T07:19:12

$(sinx-cosx)^2=1-1/csc(2x)$

The question appears to be in Spanish and I am answering in English. I hope answer will satisfy you.

$(sinx-cosx)^2$ - using $(a-b)^2=a^2+b^2-2ab$ , we get

= $sin^2x+cos^2x-2sinxcosx$

= $1-sin2x$ - (as $sin^2x+cos^2x=1$ and $sin2x=2sinxcosx$ )

= $1-1/csc(2x)$ - as $sinA=1/cscA$

Note $(sinx-cosx)^2=1-1/csc(2x)$ and not $1-1/csc^2x$ as

$1-1/csc^2x=1-sin^2x=cos^2x$

Pruebalo (sinx-cosx)^2=1-1/csc^2x(sinx-cosx)^2=1-1/csc^2x?