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if cos(alpha+beta)=0 then sin(alpha-beta)can be reduced to

options: a. cos2beta b.cosbeta c.sinalpha d.sin2alpha e.cos2alpha

We have,      cos α + β = 0⇒ cos α + β = cos 90°     as, cos 90° = 0⇒ α +  β = 90°⇒ α = 90° -  β    .............1Now, sin α -  β = sin 90° -  β -  β       using 1       ⇒ sin α -  β =  sin 90° - 2β       ⇒ sin α -  β = cos 2β     as, sin 90° - θ = cosθ                     

So, option (a) is correct.
 

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View Full Answer

It's very easy.... cos(alpha + beta) = 0

We know, cos 900 = 0 therefore (alpha + beta) = 900 i.e. alpha = (900 - beta)

Substituting value of alpha in sin(alpha - beta) we get

sin(900 -beta -beta)

sin(900 - 2beta)

cos2beta because sin(900 - theta) = cos theta

thus, ur answer is a. cos2beta

thumps up plz!!

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Wow, Yatin.......u r a star!! Here's a thubs up for you.......

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