Question

the minimum value of 27 Cosx + 81 Sinx is ?

Answer 1

Answer:

-27√10

Step-by-step explanation:

To find minimum value of aCosx + bSinx

=Multiply and divide by √a² + b²

we get

√a² + b²(a/√a² + b²Cosx + b/√a² + b²Sinx)

Let us assume sin ∅ = a/√a² + b²

cos ∅ = b/√a² + b²

so we get

√a² + b²(sin ∅Cosx + cos ∅Sinx)

=√a² + b² Sin(∅ + x)

But we now, minimum value fo Sin is -1

Hence Minimum value of aCosx + bSinx is

-√a² + b².

Hence, minimum value of 27 Cosx + 81Sinx

= -√27²+81²

=-√27²(1+9)

=-27√10.