Question

Show that sec^2x+csc^2x=sec^2xcsc^2x

Answer 1

You might know that sec²(x) - tan²(x) = 1. If we solve for sec²(x), then we obtain:

sec²(x) = 1 + tan²(x)

Then,

csc²(x)(1 + tan²(x))
==> csc²(x) + csc²(x)tan²(x)
==> csc²(x) + 1/sin²(x) * sin²(x)/cos²(x)
==> csc²(x) + 1/cos²(x)
==> csc²(x) + sec²(x)
==> RHS

I hope this helps!

Answer 2

sec^2x+csc^2x=sec^2xcsc^2x
Divide both sides by csc^2x
sec^2x+(csc^2x/csc^2x)=sec^2xcsc^2x/csc^2x
sec^2x=sec^2x
Divide both sides by sec^2x
0=0 which is a true statement.

Hope this helps :)