SOLUTION: I simply dont understand how to switch from the identites and solve these sort of questions... Prove the following identities: Tan^4=tan^2thetaxsec^2theta-sec^2theta+1 1/secthe

Question 836063: I simply dont understand how to switch from the identites and solve these sort of questions...
Prove the following identities:
Tan^4=tan^2thetaxsec^2theta-sec^2theta+1
1/sectheta+tantheta - 1/sectheta-tantheta = -2 theta
Sin (90 degrees - theta)-cos^3 theta = costheta x sign^2 theta.
Please help, thank you!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Prove the following identities:
Tan^4 = tan^2(t)*sec^2(t)-sec^2(t)+1
Note: 1+tan^2 = sec^2
----
Substitute for tan^2 to get:
(sec^2-1)^2 = (sec^2-1)(sec^2)-(sec^2)+1
(sec^2-1)^2 = sec^4-2sec^2+1
Factor the right side::
(sec^2-1)^2 = (sec^2-1)^2
----
1/sec(t)+tan(t) - 1/sec(t)-tan(t) = -2??(t)
Comment: Some function missing on the right side.
----------------
Sin(90 degrees - t)-cos^3(t) = cos(t) x sin^2(t)
----
cos(t)-cos^3(t) = cos(t)*sin^2(t)
cos(t)[1-cos^2(t)] = cos(t)*sin^2(t)
cos(t)*sin^2(t) = cos(t)(sin^2)t
===============================
Cheers,
Stan H.
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