Trigonometry
posted by Jessy on .
Prove the following trigonometric identities. please give a detailed answer because I don't understand this at all.
a. sin(x)tan(x)=cos(x)/cot^2 (x)
b. (1+tanx)^2=sec^2 (x)+2tan(x)
c. 1/sin(x) + 1/cos(x) = (cosx+sinx)(secx)(cscx)
d. tan^2 (x)(1+1/tan^2 x) = 1/(1sin^2x)
e. sin^3 (x) +cos^3 (x)/(sinx+cosx) = 1sinxcosx
f. (sinxcosx+1)/(sinx+cosx1)= (sinx+1)/cosx

if you don't understand it at all, you seriously need to review the most basic trig identities:
sin^2 + cos^2 = 1
tan = sin/cos
cot = 1/tan
With that in mind, and suppressing all the x's for ease of reading,
(a)
sin*tan = sin/cot
= sin*cot/cot^2
= sin(cos/sin) / cot^2
= cos/cot*2
(b)
(1+tan)^2
= 1+2tan+tan^2
= 1+tan^2 + 2tan
= sec^2 + 2tan
(c)
1/sin + 1/cos
= (cos+sin)/(sin*cos)
= (cos+sin)(1/cos)(1/sin)
= (cos+sin)(sec)(csc)
You try the others. These are all pretty basic. The beauty of trig functions is the hundreds of ways they can be arranged and transformed into virtually unrecognizable forms! 
Thank you for your help. It's just that I didn't take functions in grade 11 and now I'm taking Advanced Functions in grade 12 and I'm difficulty with. Thanks for your help though.