Posted by AwesomeGuy on .
Verify the identities.
1.) SIN[(π/2)X]/COS[(π/2)X]=COT X
2.) SEC(X)/CSC(X)= TAN X
3.) (1 + SIN Y)[1 + SIN(Y)]= COS²Y
4.) 1 + CSC(θ)/COS(θ) + COT(θ)= SEC θ
(Note: Just relax through verifying/solving these nice fun looking math problems! It's healthy for your brain!)

Trigonometry 
AwesomeGuy,
1.) 1/TAN[(π/2)X]=COT X BINGO! SOLVED!
2.) SEC X/CSC X
1/COS X ÷ 1/COS X
1/COS X * SIN X/1
TAN X YES BINGO! WOW! 
Trigonometry 
Steve,
(1+sin(y))(1+sin(y)
(1+sin(y))(1sin(y))
(1sin^2(y))
cos^2(y)
I think the last one has a typo or needs some parentheses. If θ=pi/4,
1 + (√2)/(1/√2) + (1) = 1  2  1 = 2
but sec(pi/4) = √2 
Trigonometry 
Reiny,
I think the last one should be
( 1 + csc(Ø) / ( cos(Ø) + cot(Ø) ) = secØ
First of all , csc(x) = cscx and cot(x) = cotx , but cos(x) = cosx
LS = (1  cscx)/( cosx  cotx)
= (1  1/sinx) / (cosx  cosx/sinx)
= [ (sinx  1)/sinx ] / [ (sinxcosx  cosx)/sinx ]
= (sinx  1) / (sinxcosx  cosx)
= (sinx  1) / (cosx(sinx  1) )
= 1/cosx
= secx
= RS