Question

$Verify \: the \: following \\ identity \colon$
${sin}^{6}\theta+{cos}^{6}\theta$=$1-3{sin}^{2}\theta{cos}^{2}\theta$

Answer 1

hope it helps!!!;!!

Answer 2

⭕️Sin6Φ=(sin²Φ)³

Similarly....

⭕️ cos6Φ=(cos²Φ)³

⭕️Now multiply expand (sin²Φ)² and (cos²Φ)²

using the identity (A+B)²=A²+2AB+B²

and simplify...

⭕️you will get answer as 2-3+1 where terms will get cancelled out !

Finally we get 0 as the answer!

hence proved !!!

\huge\bf{\boxed {\red{\mathfrak{thank \: you :)}}}}

thankyou:)