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I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ?

Solve[ γ == ArcCos[ Cos[α] Sec[θ] ] + ArcCos[ Cos[β] Sec[θ] ], θ]
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If you're looking for a numeric solution please say so explicitly. – b.gatessucks Sep 23 '12 at 10:52

2 Answers

up vote 5 down vote accepted

If you're after a symbolic solution you might try taking the Cos of both sides :

Solve[ Cos[ γ] == TrigExpand[ Cos[ ArcCos[ Cos[α] Sec[θ] ] + ArcCos[ Cos[β] Sec[θ]] ]],
         θ, Reals]

or 

Reduce[ Cos[γ] == TrigExpand[  Cos[ ArcCos[ Cos[α] Sec[θ] ] + ArcCos[ Cos[β] Sec[θ]]] ],
        θ, Reals]
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That a good idea! – chyanog Sep 23 '12 at 11:04
@chyanog You still didn't say, does the other software solve your equation symbolically ? – b.gatessucks Sep 23 '12 at 15:26
Yes,maple direct to solve it . – chyanog Sep 23 '12 at 15:33
up vote 3 down vote

Or like this:

Solve[Cos /@ (γ == ArcCos[Cos[α] Sec[θ]] + ArcCos[Cos[β] Sec[θ]] ), θ, 
 InverseFunctions -> True]
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