Question

Q. Given that sin α = √3/2 and cos β = 0 then the value of β – α is –

Answer 1

Answer:

$\bold\red{β - α = π/6}$

Step-by-step explanation:

We know that, $\pink{domain}$ and$\green{range}$ of $\purple{sine}$ and $\purple{cosine}$ functions lies between $\pink{(-π/2\:to\:+π/2)}$ and $\green{(-1\:and\:+1)}$ respectively. .

Now,

It is being given that,

sin α = √3/2

So, after analysis, we can write ,

=> sin α = sin π/3 (°.° sin π/3 = √3/2 )

Therefore,

=> α = π/3 ..............(i)

Also, it's being given that

cos β = 0

Again, after analysis, we can write,

=> cos β = cos π/2 ( °.° cos π/2 = 0 )

Therefore,

=> β = π/2 ............(ii)

Now, from eqn (i) and (ii), we get,

β - α = (π/2- π/3) = (3π - 2π)/6 = π/6

Hence,

β - α = π/6