Question

if sinA-cosA=0 then prove that sin4+cos4=1/2

Answer 1

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\bf\huge\bf\huge{\boxed{\bigstar{{SinA \:-\: cosA \:=\: 0}}}}$

⇒ sinA = cosA

$\sf{\implies\dfrac{sinA}{cosA} = 1}$        

⇒ tanA = 1

⇒ tanA = tan45°

⇒ A = 45°

= sin^2 A + cos^2 A

= sin^2 45° + cos^2 45°

$\sf{\implies(\dfrac{1}{\sqrt{2}})^2 = (\dfrac{1}{\sqrt{2}}^2)}$        

$\sf{\implies\dfrac{1}{4} + \dfrac{1}{4}}$        

$\sf{\implies\dfrac{2}{4}}$        

$\sf{\implies\dfrac{1}{2}}$

$\bf\huge\bf\huge{\boxed{\bigstar{{LHS \:=\: RHS}}}}$