Question

if sinA + cosA=a then sin^4A + cos^4A=?​

Answer 1

Sin A+ Cos A = a

Squaring both sides :

Sin²A + Cos²A +2SinACosA = a²

=> Sin A Cos A = ( a² - 1 )/2

Now :

Sin⁴A + Cos⁴A =(Sin²A + Cos²A)² - 2Sin²ACos²A

= 1 - 2(Sin ACosA)²

= 1 - 2 x{(a² - 1)/2}²

= 1 - 2 x (a⁴ -2a² + 1)/4

= 1 - (a⁴ -2a² + 1)/2

= (-a⁴ + 2a² + 1)/2