How do you prove that $(secx + tanx)/(cosx + cotx) = sinxsec^2x$ ?

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Answer 1 · 2017-03-10T01:58:55

$(1/cosx + sinx/cosx)/(cosx + cosx/sinx) = sinx(1/cos^2x)$

$((1 + sinx)/cosx)/((cosxsinx + cosx)/sinx) = sinx(1/cos^2x)$

$(1 + sinx)/cosx * sinx/(cosxsinx + cosx) = sinx(1/cos^2x)$

$(1 + sinx)/cosx * sinx/(cosx(sinx + 1)) = sinx(1/cos^2x)$

$sinx/cos^2x = sinx/cos^2x$

Hopefully this helps!

How do you prove that (secx + tanx)/(cosx + cotx) = sinxsec^2x(secx + tanx)/(cosx + cotx) = sinxsec^2x?