squaring both sides
squaring both sides
cos2+sin2+2cossin=1
cos
2
A
+
sin
2
A
+
2
cos
A
sin
A
=
1
⟹1+2cossin=1⟹2cossin=0
⟹
1
+
2
cos
A
sin
A
=
1
⟹
2
cos
A
sin
A
=
0
⟹−2cossin=0⟹1−2cossin=1
⟹
−
2
cos
A
sin
A
=
0
⟹
1
−
2
cos
A
sin
A
=
1
⟹cos2+sin2−2cossin=1
⟹
cos
2
A
+
sin
2
A
−
2
cos
A
sin
A
=
1
⟹(cos−sin2)=1
⟹
(
cos
A
−
sin
A
2
)
=
1
⟹cos−sin=±1
