trig
posted by Matt .
I do not understand these problems. :S
I'd really appreciate the help.
Use trigonometric identities to transform the left side of the equation into the right side.
cot O sin O = cos O
sin^2 O  cos^2O = 2sin^2 O 1
(tan O + cot O)/tan O = csc^2 O

for most of these you have to know your basic trig relationships
tanx = sinx/cosx ; cotx = cosx/sinx
cscx = 1/sinx ; secx = 1/cosx
sin^{2}x + cos^{2}x = 1
and its rearrangements.
so for the first :
LS = cotOsinO
= (cosO/sinO)(sinO)
= sinO
= RS
Most are this easy.
last one : (I will use x as my angle)
LS
= (sinx/cosx + cosx/ sinx)/(sinx/cosx)
= (sin^{2}x + cos^{2}x)/(sinxcosx) x (cosx/sinx)
= 1/(sinxcosx)(cosx/sinx)
= 1/sin^{2}x
= csc^{2}x
= RS
try the second one, it is even easier. 
solve for x to the nearest thousandth: 2tan square x5tan x1

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