Test 40
1.
\(\samefrac{\sin15^\circ\cos45^\circ+\sin45^\circ\cos15^\circ}{\cos55^\circ\cos25^\circ+\sin55^\circ\sin25^\circ}=?\)
A) \(\sqrt2\)B) \(\sqrt3\)C) \(\samefrac{\sqrt3}{2}\)D) \(\samefrac12\)E) \(1\)
2.
\(\cos(\operatorname{arccot}\samefrac12)=?\)
A) \(\samefrac1{\sqrt5}\)B) \(\samefrac2{\sqrt5}\)C) \(-\samefrac1{\sqrt5}\)D) \(-\samefrac2{\sqrt5}\)E) \(-1\)
3.
ABCDEFGH is a cube. ABCD is the bottom face and EFGH is vertically above A, B, C, D respectively.
\(m(DBH)=\alpha\)
\(\Rightarrow\cot\alpha=?\)
A) \(\samefrac{\sqrt2}{2}\)B) \(\samefrac{\sqrt3}{2}\)C) \(\samefrac1{\sqrt3}\)D) \(\samefrac2{\sqrt3}\)E) \(\sqrt2\)
4.
\(0\le\alpha\le90^\circ\)
\(\samefrac{\sqrt2\sin3^\circ\cos11^\circ+\sqrt2\sin11^\circ\cos3^\circ}{4\cos83^\circ\cos7^\circ}=\sin\alpha\)
\(\Rightarrow\alpha=?\)
A) \(15^\circ\)B) \(30^\circ\)C) \(45^\circ\)D) \(60^\circ\)E) \(90^\circ\)
5.
\(\cos(\samefrac\pi2+a)=K\)
Which of the following is equal to K?
A) \(\sin(\samefrac\pi2-a)\)B) \(\cos(2\pi-a)\)C) \(\cos(-a)\)D) \(\cos a\)E) \(\sin(-a)\)
6.
\(a=\sin7^\circ\)
\(b=\sin82^\circ\)
\(c=\sin105^\circ\)
Which ordering is correct?
A) \(aB) \(aC) \(bD) \(bE) \(c
7.
\(\cos^2(x-y)+\sin^2(x+y)=?\)
A) \(1+\cos^2x\sin^2x\)B) \(1+\sin(2x)\cos(2x)\)C) \(1+\sin(2x)\sin(2y)\)D) \(1+\cos(2x)\cos(2y)\)E) \(1-\sin(2x)\sin(2y)\)
8.
ABCD is a rectangle. E lies on DC.
\(|AD|=4,\ |AB|=10\)
\(|EC|<|DE|\)
\(m(DAE)=m(CEB)=\alpha\)
\(\Rightarrow\cot\alpha=?\)
A) \(\samefrac18\)B) \(\samefrac14\)C) \(\samefrac12\)D) \(2\)E) \(4\)