Question

If sin a - cos a=0 then the value of sin ^4 a+ cos^4 a is

Answer 1

$sin a \: - cosa = 0$

$on \: squaring \: both \: side \: we \: get$

$(sina - cos) {}^{2} = (0) {}^{2}$

$sin {}^{2} a + cos {}^{2} a - 2sina \: cosa = 0$

$sin {}^{2} a + cos {}^{2} a = 2sina \: cosa$

$again \: squaring \: both \: side$

$(sin {}^{2} a + cos {}^{2} a) {}^{2} = (2sina \: cosa) {}^{2}$

$sin {}^{4} a + cos {}^{4} a + 2sin {}^{2} a \: cos {}^{2} a \: = 4sin {}^{2} a \: cos {}^{2} a$

$sin {}^{4} a \: + cos {}^{4} a = 4sin {}^{2} a \: cos {}^{2} a - 2sin {}^{2} a \: cos {}^{2} a$

$sin {}^{4} a \: + cos {}^{4} a = 2sin {}^{2} a \: cos {}^{2} a$

$thanks$

Answer 2

sinA=cosA

or sin45=cos45

A=45

SIN^4A+COS^4A= SIN^4(45)+COS^4(45)= {(1/2)^(1/2)}4 + ​{(1/2)^(1/2)}4

=1/2