Could someone please demonstrate to me how to solve these equations:

a) arccos(x) + arccos(x*sqrt(3)) = pi/2

b) 2arcsin(x*sqrt(6)) + arcsin(4x) = pi/2</SPAN>

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- Nov 15th 2009, 10:09 AMSunyataHard Questions on Inverse Trigonometry
Could someone please demonstrate to me how to solve these equations:

a) arccos(x) + arccos(x*sqrt(3)) = pi/2

b) 2arcsin(x*sqrt(6)) + arcsin(4x) = pi/2</SPAN> - Nov 15th 2009, 10:16 AMskeeter
see this thread ... solution process is the same.

http://www.mathhelpforum.com/math-he...ease-help.html - Nov 15th 2009, 12:24 PMSoroban
Hello, Sunyata!

Quote:

The equation becomes: .

Take the cosine: .

. . which becomes: .

Substitute [1]: .

. . . . . .

Square both sides: .

. . Therefore: .

- Nov 15th 2009, 12:53 PMskeeter
is an extraneous solution

- Nov 15th 2009, 01:55 PMSoroban
Absolutely right, skeeter . . . *blush*

Thanks for the correction.

- Nov 15th 2009, 04:21 PMxwrathbringerx
Hmmm how exactly do u find the domain for x, skeeter and Soroban?

- Nov 15th 2009, 04:25 PMskeeter
- Nov 15th 2009, 04:28 PMxwrathbringerx
Oops i mean domain for x. (Doh)

Sori - Nov 15th 2009, 05:01 PMskeeter
start a new thread.

- Nov 15th 2009, 06:16 PMSunyata
ARGH I get a massive equation for the 2nd question which I cannot solve...

- Nov 15th 2009, 07:19 PMxwrathbringerx
Ummm for the 2nd question, am i MEANT to get 7744x^10 - 3008x^6 + 176 x^5 + 240x^4 - 8x^2 - 8x + 1 = 0 because I keep on getting it, which I've been trying to solve for ages (Sleepy)