mathslover
tan A = -1/2 , tan B = -1/3 , then A+B = ?
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mathslover
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@calculusfunctions sir.
mathslover
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I had come up with : tan (A+B) = -1
mathslover
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so (A+B) = ?
Coolsector
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A+B = -45 + 180 * k
mathslover
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is it, 7pi /4
waterineyes
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\[\tan(A+B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A) \cdot \tan(B)}\]
Coolsector
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-45 = pi/4
180 = pi
so
-pi/4 + pi = 3pi/4
-pi/4 + 2pi = 7pi/4
and so on..
waterineyes
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If you calculated it right then:
\[A+B= \tan^{-1}(-1)\]
Coolsector
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so 7pi/4 is one possibility
03453660
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\[A+B = \tan^{-1}\frac{ -1 }{ 2 }+\tan^{-1} \frac{ -1 }{ 3 }\]
mathslover
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so it can be : 3 pi / 4, 7pi/4 , . ...
It can not be 5 pi / 4 because it will be positive for tan.
mathslover
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But the book says that the answer is : d) none
Options were :
i) pi/4
ii) 3 pi/4
iii) 5 pi/4
iv) none.
mathslover
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So it will be 3 pi/4 ? or none?
hartnn
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it will be 3pi/4
are any constraints given?
mathslover
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constraints?
hartnn
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like A+B should be between 0 to 90 or something like this ?
hartnn
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else 3pi/4 is correct
mathslover
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ok thanks a lot @hartnn :)
sara12345
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wud tan(A+B) formula work for all angles
hartnn
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yes.
sara12345
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ok thank you :D
waterineyes
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\[\pi - \frac{\pi}{4} = \frac{3 \pi}{4}\]
waterineyes
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There was some mistake in the formula that I had written above..
That day I was looking for the same and now I have found it :
\[\tan^{-1}(-x) = \pi - \tan^{-1}(x)\]