Question

If sinA-cosA=0 then show that sin^4A+cos^4A=1/2

Answer 1

hope it's clear
...........

Answer 2

$Given \: sin A - cos A = 0$

$\implies sinA = cosA$

$\implies cos (90 - A ) = cosA$

$\implies 90 - A = A$

$\implies 90 = A + A$

$\implies 90 = 2A$

/* Dividing both sides by 2 , we get */

$\implies 45 = A\: ---(1)$

$LHS = sin^{4} A + cos^{4} A \\= sin^{4} 45\degree + cos^{4} 45\degree \\= \Big( \frac{1}{\sqrt{2}}\Big)^{4} + \Big( \frac{1}{\sqrt{2}}\Big)^{4} \\= \frac{ 1}{4} + \frac{1}{4} \\= \frac{2}{4} \\= \frac{1}{2} \\= RHS$

Therefore.,

$\red { sin^4 A+cos^4 A} \green { = \frac{1}{2} }$

•••♪