Question

Solve plzz........ Only two questions - (attempt any one)

Answer 1

Answer:

Option(B)

Step-by-step explanation:

Given A = sin²θ + cos⁴θ

= 1 - cos²θ + cos⁴θ

It can be written as,

= 1 - 2 * cos²θ/2 + (cos²θ)²

It can be written as

= (3/4 + 1/4) - 2 cos²θ/2 + (cos²θ)²

= (3/4) + (1/4) - 2 cos²θ/2 + (cos²θ)²

= (3/4) + (1/2)² - 2 cos²θ/2 + (cos²θ)²

We know that a² - 2ab + b² = (a -  b)²

= (3/4) + (cos²θ - 1/2)²

Range of cosθ is [0,1]

Minimum value = 1/2, 3/4

Maximum value = 0,1

∴ Thus, 3/4 ≤ A ≤ 1.

Hope it helps!

Answer 2

Step-by-step explanation:

A = cos^4x + sin^2 x

= (1-sin^2 x)^2 + sin^2x

= 1 + sin^4 x -sin^2 x

let sin^2 x = p

A = (p - 1/2)^2 + 3/4

0 (<or=) p (<or=) 1

so a is between 3/4 to 1.