Given the following identity, secxcscx(tanx+cotx) = 2 + tan^2(x) + cot^2(x):
Prove the identity by completing the table below, indicating the steps on the left and the reasoning on the right.

Question

anonymous · Answer

$$secxcscx(tanx+cotx) = 2 + \tan^2x + \cot^2x$$

anonymous · Answer

I'm exactly sure how I'm supposed to start...

ankit042 · Answer

start by expanding the terms

ankit042 · Answer

you will get secXcscXtanX +secXcscXcotX
now convert everything in terms of sinX and cosX

anonymous · Answer

$$\csc^2(x)+\sec^2(x) $$this is what I got!

anonymous · Answer

$$\sec x \csc x \left( \tan x+\cot x \right)=\frac{ 1 }{\cos x \sin x }\left( \frac{ \sin x }{\cos x }+\frac{\cos x }{\sin x } \right)$$
$$=\frac{ 1 }{\cos ^{2}x }+\frac{ 1 }{\sin ^{2} x}$$
$$=\sec ^{2}x+\csc ^{2}x=1+\tan ^{2}x+1+\cot ^{2}x=R.H.S$$

ankit042 · Answer

yes now you can solve the right hand side use 1+tan^2=sec^ and 1+csc^2X=csc^2X

anonymous · Answer

$$\csc^2(x) \sec^2(x) $$ !!!

anonymous · Answer

But then which parts go in the boxes? |dw:1376423804861:dw|