Question

Set sin2a = 3/5 then find sin^4(a)+cos^4(a)

pls. give me answer.​

Answer 1

`sin^4(a)+cos^4(a)=(41)/(50)`

Explanation:

we have

`sin^4(a)+cos^4(a)`

Complete the square

`sin^4(a)+cos^4(a)=(sin^2(a)+cos^2(a))^2-2sin^2(a)cos^2(a)`

Remember that

`sin^2(a)+cos^2(a)=1`

so

`sin^4(a)+cos^4(a)=1-2sin^2(a)cos^2(a)`

Rewrite

`sin^4(a)+cos^4(a)=1-2(sin(a)cos(a))^2`

we know that

`sin(2a)=2sin(a)cos(a)\\\\(1)/(2)sin(2a)=sin(a)cos(a)`

In this problem we have

`sin(2a)=(3)/(5)`

so

`(1)/(2)sin(2a)=(1)/(2)((3)/(5))=(3)/(10)`

`sin(a)cos(a)=(3)/(10)`

substitute

`sin^4(a)+cos^4(a)=1-2(sin(a)cos(a))^2`

`sin^4(a)+cos^4(a)=1-2((3)/(10))^2`

`sin^4(a)+cos^4(a)=1-(18)/(100)`

`sin^4(a)+cos^4(a)=(82)/(100)`

simplify

`sin^4(a)+cos^4(a)=(41)/(50)`