Question

SinA + cosA = 1 Find the value of cos^2A + cos^4A =?

Answer 1

`rarrcos^2A+cos^4(A)=0`

Explanation:

Given,

`rarrsinA+cosA=1`

`rarrsin90^@+cos90^@=1+0=1`

It means `90^@` is the root of the equtaion

Now,

`cos^2A+cos^4(A)=(cos90^@)^2+(cos90^@)^4=0^2+0^4=0`

Answer 2

0, or 2

Explanation:

`sin A + cos A = sqrt2cos (A - pi/4) = 1`
`cos (A - pi/4) = 1/sqrt2 = sqrt2/2`
Trig table and unit circle give 2 solutions:
`A - pi/4 = +- pi/4`

a. `A = pi/4 + pi/4 = pi/2`
`cos A = cos (pi/2) = 0` --> `cos^2 A = cos^4 A = 0`
`cos^2 A + cos^4 A = 0`
b. `A - pi/4 = - pi/4` --> `A = -pi/4 + pi/4 = 0`
`cos A = 1` --> `cos ^2 A = cos^4 A = 1`
`cos^2 A + cos^4 A = 1 + 1 = 2.`