If A+B=3π and cosA+cosB=1, then which of the following are true:

Ans. (b), (c)From the given relation, we have 2cos2A+B cos2A−B=1Or 2cos30ocos2A−B =1∴cos2A−B =3 1∴cos(A−B) =cos22A−B−1=2.31−1=−31⇒(b)Again ∣cosA−cosB ∣=2sin2A+B sin2B−A =2sin30o1−cos22A−B =11−31 =32

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If A+B= { }{ 3 } and { A } + { B } =1 , then which of the f

Question

If $A + B = \frac{π}{3}$ and $cos A + cos B = 1$ , then which of the following are true:

cos (A - B) = \frac{1}{3}

cos (A - B) = - \frac{1}{3}

∣ cos A - cos B ∣ = 2/3

∣ cos A - cos B ∣ = \frac{1}{3}

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Emma Discussed

A + B = \frac{π}{3}

and

cos A + cos B = 1

, then which of the following are true:

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Ans.

(b)

(c)

From the given relation, we have

2 cos \frac{A + B}{2} cos \frac{A - B}{2} = 1

2 cos 30^{o} cos \frac{A - B}{2} = 1

∴ cos \frac{A - B}{2} = \frac{1}{3}

∴ cos (A - B) = cos^{2} \frac{A - B}{2} - 1 = 2. \frac{1}{3} - 1 = - \frac{1}{3} \Rightarrow (b)

Again

∣ cos A - cos B ∣ = 2 sin \frac{A + B}{2} sin \frac{B - A}{2}

= 2 sin 30^{o} 1 - cos^{2} \frac{A - B}{2} = 1 1 - \frac{1}{3} = \frac{2}{3}

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Question Text	If $A + B = \frac{π}{3}$ and $cos A + cos B = 1$ , then which of the following are true:
Answer Type	Text solution:1
Upvotes	150

If A+B=3π ​ and cosA+cosB=1, then which of the following are true:

Text solutionVerified

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If $A + B = \frac{π}{3}$ and $cos A + cos B = 1$ , then which of the following are true: