[MOVED] Show that (cot(x)+tan(x))^2 = csc^2(x) + sec^2(x)

[nalani]

We just began learning about cotangents, cosecants, etc, and I'm having some troble on the following problem:

. . .Show that (cot(x)+tan(x))^2 = csc^2(x) + sec^2(x)

The only thing I've been able to do is rewrite it as:

. . .(cos(x)/sin(x)) + sin(x)/cos(x) = (1/sin^2(x)) + (1/cos^2(x))

Hints, please?

 

[galactus]

\(\displaystyle \L\\(cot(x)+tan(x))^{2}=csc^{2}(x)+sec^{2}(x)\)

Expand left side:

\(\displaystyle \L\\cot^{2}(x)+2cot(x)tan(x)+tan^{2}(x)\)

identity:\(\displaystyle cot(x)tan(x)=1\)

\(\displaystyle \L\\cot^{2}(x)+2+tan^{2}(x)\)

Now, can you finish?.

Remember that \(\displaystyle cot^{2}(x)+1=csc^{2}(x)\;\ and \;\ tan^{2}(x)+1=sec^{2}(x)\)

 

[nalani]

thanks!!!