UPSEE Solved Model Paper 6

Here we can find the value of sin(α +2β).
We know that
sin(180° - a) = sin a
Given,
Cos (α + β) = 0
cos (α + β) = cos

π

2

⇒ α + β =

π

2

(since, cos

π

2

= cos 90 = 0)
(Multiplying β = π/2 - α)
⇒ 2β = 2

π

2

−2α
⇒ α + 2β = π − 2α + α
⇒ α + 2β = π – α
⇒ Sin (α + 2β) = Sin (π - α)= Sin α
[Since, sin(π - θ) = sinθ]
Therefore ,
sin(α +2β) = sin α
Hence,
If Cos (α + β) = 0, then sin(α +2β) = sin α
In same question, there are two answers
Another answer :
Given,
α + β =

π

2

sin (α + β + β)
= (sin

π

2

+β)
(Since α + β = π/2 , given)
= cos β
(Since sin (90 + θ) = cos θ)