Question

a coseΦ + b sineΦ= c if α,β is the sollution of Φ then prove
sin(α+β)=2ab/(a^2 + b^2)​

Answer 1

Step-by-step explanation:

α,β)=

∣

∣

∣

∣

∣

∣

∣

∣

cosα

sinα

cos(α+β)

−sinα

cosα

−sin(α+β)

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=cosα(cosα+sin(α+β))+sinα(sinα−cos(α+β))−(sinαsin(α+β)+cosαcos(α+β))

=1+sin(α+β−α)−cos(α+β−α)

=1+sinβ−cosβ

⇒ϕ(α,β) is independent of α.

∴f(300,200)=f(400,200) and f(100,200)=f(200,200)

Hence, options A and C.