Hey.
That is what im having trouble sorting out. I know its something to do with the quadratic formula but its just not clicking in my head.Code:2Ln2 - Ln(x-1) = ln(2x)
also, i cant seem to finish this off:
This is what i have so far:Code:Prove that (1/cot^2 θ) - (1/csc^2 θ) = (sin^4 θ)/(cos^2 θ)
i am stuck there... unless of course the actually DO add together to makeCode:-> (1/(1/tan^2 θ)) - (1/(1/sin^2 θ)) -> 1/(tan^2 θ - sin^2 θ) -> (1/((cos^2 θ)/(sin^2 θ))) - (1/sin^2 θ) -> ((sin^2 θ)/(cos^2 θ)) + ((sin^2 θ)/ 1)
Any help would be greatly appreciated!Code:(sin^4 θ)/(cos^2 θ)
i still dont understand what's been done:
-> (1/(1/tan^2 θ)) - (1/(1/sin^2 θ))
-> tan^2θ - sin^2 θ
-> sin^2 θ /cos^2 θ - sin^2 θ <<here
-> sin^2θ( 1/cos^2 θ -1) <<here
-> sin^2 θ ( sec^2 θ -1) <<here
-> sin^2θ (tan^2 θ) <<here
-> sin^2 θ x sin^2 θ/cos^2 θ
-> sin^4 θ/cos^2 θ
like how did
sin^2 θ /cos^2 θ - sin^2 θ
become:
sin^2θ( 1/cos^2 θ -1) ?
and so on so forth?
Thanks if someone could clear this up!
Take common
-------(1)
Using the rule that
sec(x) = 1/cos(x)
Replace by
= sin^2 θ ( sec^2 θ -1)......................(2)
Using the property that
sec^2 (x) = 1 + tan^2 (x)
Replace by
which gives
-----------------------------
Tell the step you fail to understand now