Giải các phương trình ở công thức bội cho cos2(x) và sin2(x), thu được:

sin 2 ⁡ ( x ) = 1 − cos ⁡ ( 2 x ) 2 {\displaystyle \sin ^{2}(x)={1-\cos(2x) \over 2}} cos 2 ⁡ ( x ) = 1 + cos ⁡ ( 2 x ) 2 {\displaystyle \cos ^{2}(x)={1+\cos(2x) \over 2}} tan 2 ⁡ ( x ) = 1 − cos ⁡ ( 2 x ) 1 + cos ⁡ ( 2 x ) {\displaystyle \tan ^{2}(x)={1-\cos(2x) \over 1+\cos(2x)}} sin 2 ⁡ ( x ) cos 2 ⁡ ( x ) = 1 − cos ⁡ ( 4 x ) 8 {\displaystyle \sin ^{2}(x)\cos ^{2}(x)={1-\cos(4x) \over 8}} sin 3 ⁡ ( x ) = 3 sin ⁡ ( x ) − sin ⁡ ( 3 x ) 4 {\displaystyle \sin ^{3}(x)={\frac {3\sin(x)-\sin(3x)}{4}}} cos 3 ⁡ ( x ) = 3 cos ⁡ ( x ) + cos ⁡ ( 3 x ) 4 {\displaystyle \cos ^{3}(x)={\frac {3\cos(x)+\cos(3x)}{4}}} sin 4 ⁡ ( x ) = 1 cos ⁡ ( 4 x ) − 4 cos ⁡ ( 2 x ) + 3 8 {\displaystyle \sin ^{4}(x)={\frac {1\cos(4x)-4\cos(2x)+3}{8}}} cos 4 ⁡ ( x ) = 1 cos ⁡ ( 4 x ) + 4 cos ⁡ ( 2 x ) + 3 8 {\displaystyle \cos ^{4}(x)={\frac {1\cos(4x)+4\cos(2x)+3}{8}}}