Property 17
Sum and Difference Formulas
\(\blacksquare\quad \sin(\alpha+\beta)=\sin\alpha\cdot\cos\beta+\cos\alpha\cdot\sin\beta\)
\(\blacksquare\quad \sin(\alpha-\beta)=\sin\alpha\cdot\cos\beta-\cos\alpha\cdot\sin\beta\)
\(\blacksquare\quad \cos(\alpha+\beta)=\cos\alpha\cdot\cos\beta-\sin\alpha\cdot\sin\beta\)
\(\blacksquare\quad \cos(\alpha-\beta)=\cos\alpha\cdot\cos\beta+\sin\alpha\cdot\sin\beta\)
\(\blacksquare\quad \tan(\alpha+\beta)=\samefrac{\tan\alpha+\tan\beta}{1-\tan\alpha\cdot\tan\beta}\)
\(\blacksquare\quad \tan(\alpha-\beta)=\samefrac{\tan\alpha-\tan\beta}{1+\tan\alpha\cdot\tan\beta}\)
\(\blacksquare\quad \cot(\alpha+\beta)=\samefrac{\cot\alpha\cdot\cot\beta-1}{\cot\alpha+\cot\beta}\)
\(\blacksquare\quad \cot(\alpha-\beta)=\samefrac{\cot\alpha\cdot\cot\beta+1}{\cot\beta-\cot\alpha}\)
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.
\(0<a+b<\samefrac\pi2\)
\(\cot a=3\)
\(\cot b=2\)
\(\Rightarrow a+b=?\)
13.
\(\cot a=\samefrac12,\ \cot b=\samefrac13\)
\(\cot(a-b)=?\)
14.
\(\cot(-75^\circ)=?\)
15.
\(\Rightarrow\tan\alpha=?\)
16.
ABCD square
\(\Rightarrow\cot\alpha=?\)
17.
ABCD square
\(\Rightarrow\tan\alpha=?\)
18.
ABCD square
\(\Rightarrow\sin\alpha=?\)
19.
\([AB]\perp[BC]\)
\(\Rightarrow\tan\alpha=?\)
20.
ABCD square
\(\Rightarrow\cot\alpha=?\)
21.
\(|AC|=|BC|\)
\(\tan(\widehat C)=\samefrac34\)
\(\Rightarrow\cot(\widehat A)=?\)
22.
\(\Rightarrow\tan\alpha=?\)
23.
ABCD (square)
EFKC (square)
\(|BE|=|EC|\)
\(\Rightarrow\tan(\widehat{DEK})=?\)