SOLUTION: Trigonometry Find the exact value of: inverse cos(0) inverse cos (cos 4pi/3) Simplify cos x/sin x *(tan x + cos x) Simplify (sinx squared - 1)*(tanx squared - 1)

Algebra ->  Finance -> SOLUTION: Trigonometry Find the exact value of: inverse cos(0) inverse cos (cos 4pi/3) Simplify cos x/sin x *(tan x + cos x) Simplify (sinx squared - 1)*(tanx squared - 1)       Log On


   

Question 1130046: Trigonometry
Find the exact value of:
inverse cos(0)
inverse cos (cos 4pi/3)
Simplify cos x/sin x *(tan x + cos x)
Simplify (sinx squared - 1)*(tanx squared - 1)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
The inverse cosine is taken in QI and QII between 0 and p.



%22%22=%22%22pi%2F2



First find:



%22%22=%22%22-1%2F2



Then



%22cos%22%5E%28-1%29%28cos%284pi%2F3%29%5E%22%22%29%22%22=%22%22%22cos%22%5E%28-1%29-1%2F2%22%22=%22%222pi%2F3



--------------------------------------------------------



expr%28cos%28x%29%2Fsin%28x%29%29%2A%28tan%28x%29%5E%22%22+%2B+cos%28x%29%29 







Distribute











1%2B+cos%5E2%28x%29%2Fsin%5E%22%22%28x%29



1%2B+%281-sin%5E2%28x%29%29%2Fsin%5E%22%22%28x%29



1%2B+1%2Fsin%28x%29-sin%5E2%28x%29%2Fsin%5E%22%22%28x%29



1%2B+csc%28x%29-sin%5Ecross%282%29%28x%29%2Fcross%28sin%5E%22%22%28x%29%29



1%2Bcsc%28x%29-sin%28x%29



-----------------------------------



%28sin%5E2%28x%29%5E%22%22%5E%22%22+-+1%29%2A%28tan%5E2%28x%29%5E%22%22%5E%22%22+-+1%29



%28-1%2Bsin%5E2%28x%29%5E%22%22%5E%22%22%29%2A%28tan%5E2%28x%29%5E%22%22%5E%22%22+-+1%29



-1%281-sin%5E2%28x%29%5E%22%22%5E%22%22%29%2A%28tan%5E2%28x%29%5E%22%22%5E%22%22+-+1%29



-1%28cos%5E2%28x%29%5E%22%22%5E%22%22%29%2A%28tan%5E2%28x%29%5E%22%22%5E%22%22+-+1%29



-cos%5E2%28x%29%28tan%5E2%28x%29%5E%22%22%5E%22%22+-+1%29



-cos%5E2%28x%29%28sin%5E2%28x%29%2Fcos%5E2%28x%29+-+1%29



Distribute:



-cos%5E2%28x%29expr%28sin%5E2%28x%29%2Fcos%5E2%28x%29%29+%2B+cos%5E2%28x%29







-sin%5E2%28x%29%2Bcos%5E2%28x%29



cos%5E2%28x%29-sin%5E2%28x%29



cos%282x%29



Edwin