Question

Set sin2a = 3/5 then find sin^4(a)+cos^4(a)pls. give me answer.​

Answer 1

Answer:

$sin^4(a)+cos^4(a)=\frac{41}{50}$

Step-by-step 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

$sin(2a)=2sin(a)cos(a)\\\\\frac{1}{2}sin(2a)=sin(a)cos(a)$

In this problem we have

$sin(2a)=\frac{3}{5}$

so

$\frac{1}{2}sin(2a)=\frac{1}{2}(\frac{3}{5})=\frac{3}{10}$

$sin(a)cos(a)=\frac{3}{10}$

substitute

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

$sin^4(a)+cos^4(a)=1-2(\frac{3}{10})^2$

$sin^4(a)+cos^4(a)=1-\frac{18}{100}$

$sin^4(a)+cos^4(a)=\frac{82}{100}$

simplify

$sin^4(a)+cos^4(a)=\frac{41}{50}$