Question

if sin ( alpha+beta)=1 and cos ( alpha-beta)=1 where alpha +beta<90 the the value of alpha and beta respectively equal to ​

Answer 1

Answer:

The value of \cos(\alpha - \beta)\ is "" < strong > [tex]\dfrac{\sqrt{3} }{2}cos(α−β) is""<strong>[tex]

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Step-by-step explanation:

We have,\sin(\alpha +\beta)\ = 1)sin(α+β) =1) \

⇒\sin(\alpha +\beta)\ = \sin(90\degree)sin(α+β) =sin(90°) \

∴ α + β = 90°

Let α = 60° and β = 30°

∴ \cos(\alpha - \beta)\ = \cos(60\degree - 30\degree) cos(α−β) =cos(60°−30°)

⇒ < /strong > \cos(\alpha - \beta)\ = \cos(30\degree)\ < strong > =\dfrac{\sqrt{3} }{2}</strong>cos(α−β) =cos(30°) <strong>=

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Hence, the value of \cos(\alpha - \beta)\ is " < strong > [tex]\dfrac{\sqrt{3} }{2}cos(α−β) is"<strong>[tex]

2

3

".

Step-by-step explanation:

i hope its help full to you