Question

What is the value of Sin^4x+cos^4x

Answer 1

Answer:

Answer. Now,the maximum and minimum values of sin2x are +1 &-1 respectively . But here (sin2x)^2 is always positive so,the minimum value of(sin2x)^2 is 0. So ,the maximum value of sin^4x +cos^4x is 1–0=1(one).

Step-by-step explanation:

Answer 2

Answer:

sin⁴x + cos⁴x

= (cos²x + sin²x)² - 2*sin²x*cos²x

= 1 - ½*(2*sinx*cosx)²

= 1 - ½*sin²2x

= 1 - ¼*(1 - cos4x)

= ¾ - ¼*cos4x

So maximum value of expression is 1

minimum value of the expression is ½

Step-by-step explanation:

Formulae used

Sin2x = 2*sinx*cosx

1 - cos4x = 2*sin²2x

-1 ≤ cos4x ≤ 1

i hope this helps u