Here is the first one.
Hi, I just got slipped up on a few problems here, not sure which angle to attack from all thetas will be x, since i am ignorant about symbols, etc
Simplify
1. (2sinxcosx + 2cosx)/(cosx((sin^2)x - 1))
2. (tanx + tanxsinx - cosxsinx)/(sinxtanx)
3. [(coxtanx)/tan(90degrees - x)] - 1/(sin(90degrees - x))
4. [(2 + (tan^2)x)/(sec^2)x] - 1
Any help is much appreciated
Thanks so much
PerfectHacker's solution made the original more complex.
Here is one way.
(2sinxcosx + 2cosx)/(cosx((sin^2)x - 1))
= 2cosX(sinX +1) / cosX(sin^2(X) -1)
The cosX cancels out,
= 2(sinX +1) / (sinX +1)(sinX -1)
The (sinX +1) cancels out,
= 2 / (sinX -1) -----------------------answer.
Hello, leviathanwave!
Code:tan(x) + tan(x)·sin(x) - cos(x)·sin(x) 2. --------------------------------------- sin(x)·tan(x)
Multiply top and bottom by cos(x):Code:sin(x) + sinē(x) - sin(x)·cosē(x) --------------------------------- sinē(x) sin(x)·[1 + sin(x) - cosē(x)] = ----------------------------- sinē(x) 1 - cosē(x) + sin(x) = -------------------- sin(x) sinē(x) + sin(x) = ------------------ sin(x) sin(x)·[sin(x) + 1] = -------------------- sin(x) = sin(x) + 1
Hello again, leviathanwave!
Code:2 + tanē(x) 4. ------------ - 1 secē(x)Code:1 + 1 + tanē(x) 1 + secē(x) --------------- - 1 = ----------- - 1 secē(x) secē(x) 1 secē(x) 1 = ------- + ------- - 1 = ------- + 1 - 1 secē(x) secē(x) secē(x) 1 = ------- = cosē(x) secē(x)