Question

Sin^4x+cos^4. =1
______________
1-2sin^2x×cos^2x

Answer 1

to prove:-
sin⁴x+cos⁴x
__________ =1
1 - 2 sin²xcos²x
proof:-
L.H.S
(sin²x)²+(cos²x)² _____________
1-2sin²xcos²x

(sin²x+cos²x)²-2sin²xcos²x
_____________________ [∵a²+b²=(a+b)²-2ab]
1-2sin²xcos²x

1-2sin²xcos²x
___________ [∵sin²x+cos²x=1]
1-2sin²xcos²x

=1
∴L.H.S=R.H.S[∴Proved]