Question

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/(1-sin^2x)
e. sin^3 (x) +cos^3 (x)/(sinx+cosx) = 1-sinxcosx
f. (sinx-cosx+1)/(sinx+cosx-1)= (sinx+1)/cosx

Answer 1

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!

Answer 2

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.