how would you simplify this trig. equation.
(1+sec2x)(cot2x)
*note: the blue 2's are squared.
i did it and the final answer i got is 2cot2x
Here is one way.Originally Posted by CONFUSED_ONE
Let U = (1 +sec^2(x))*cot^2(x)
So,
U = cot^2(x) +[sec^2(x) *cot^2(x)]
U = cot^2(x) + [1/cos^2(x) *cos^2(x)/sin^2(x)]
U= cot^2(x) +1/sin^2(x)
U = cot^2(x) +csc^2(x) --------(i)
The trig identity,
sin^2(x) +cos^2(x) = 1
Divide both sides by sin^2(x),
1 +cot^2(x) = csc^2(x)
Rearrange,
1 = -cot^2(x) +csc^2(x) ---------(ii)
Add (i) and (ii),
U +1 = 2csc^2(x)
Hence,
U = 2csc^2(x) -1
Therefore,
(1 +sec^2(x))*cot^2(x) = 2csc^2(x) -1 -----------answer.
Or,
Subtract (ii) from (i),
U -1 = 2cot^2(x)
Hence,
U = 2cot^2(x) +1
Therefore,
(1 +sec^2(x))*cot^2(x) = 2cot^2(x) +1 -----------answer.