Property 17
Sum and Difference Formulas
\(\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta\)
\(\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta\)
\(\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta\)
\(\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta\)
\(\tan(\alpha+\beta)=\samefrac{\tan\alpha+\tan\beta}{1-\tan\alpha\tan\beta}\)
\(\tan(\alpha-\beta)=\samefrac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}\)
1.
\(\cos(30^\circ+45^\circ)=?\)
2.
\(\sin75^\circ=?\)
3.
\(\cos15^\circ=?\)
4.
\(\cos20^\circ\cos10^\circ-\sin20^\circ\sin10^\circ=?\)
5.
\(\sin45^\circ\cos15^\circ+\sin15^\circ\cos45^\circ=?\)
6.
\(10x=\pi\)
\(\cos3x\cos2x-\sin3x\sin2x=?\)
7.
\(\sin(40^\circ+2x)\cos(20^\circ-2x)+\sin(20^\circ-2x)\cos(40^\circ+2x)=?\)
8.
\(\tan75^\circ=?\)
9.
\(\tan15^\circ=?\)
10.
\(\samefrac{\tan70^\circ+\tan65^\circ}{1-\tan70^\circ\tan65^\circ}=?\)
11.
\(\tan x=\samefrac12,\ \cot y=\samefrac13\)
\(\cot(x+y)=?\)
12.
\(0
\(a+b=?\)
13.
\(\cot a=\samefrac12,\ \cot b=\samefrac13\)
\(\cot(a-b)=?\)
14.
\(\cot(-75^\circ)=?\)