Trigonometry

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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

  • Trigonometry -

    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!

  • Trigonometry -

    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.

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