Question

If sinx+cosx=1/2,then sin^4x+cos^4x as a rational number equals?

Answer 1

Answer:

=23/32

Step-by-step explanation:

sinx+cosx=1/2

Squaring on both sides

(sinx+cosx)^2=(1/2)^2

sin^2x+2sinx.cosx+cos^2x=1/4

{Since.. sin^2+cos^2=1 }

1+2sinx.cosx=1/4

2sinx.cosx=1/4–1

2sinx.cosx=-3/4

sinx.cosx=-3/4/2

sinx.cosx=-3/8

Now, To find sin^4x+cos^4x

(Sin^2x)^2 + (cos^2x)^2

Using a^2+b^2=(a+b)^2–2ab

=(sin^2x+cos^2x)^2 - 2.sin^2x.cos^2x

=1^2 - 2.sinx.sinx.cosx.cosx

=1–2(sinx.cosx)^2

=1–2.(-3/8)^2

=1–2(9/64)

=1–18/64

=(64–18)/64

=46/64

=23/32