Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org
• Trigonometry
• Trigonometric identities test
• Double and half angle identities

# Double and half angle identities

ans:
syntax error
C
DEL
ANS
±
(
)
÷
×
7
8
9
4
5
6
+
1
2
3
=
0
.
auto next question
calculator
•  Question 1: 1 pts Which expression represent double angle identity for sine function, $\sin 2u?$
 $\cos^{2}u-\sin^{2}u$ $\sin^{2}u+\cos^{2}u$ $-2\sin u \cos u$ $2\sin u \cos u$
•  Question 2: 1 pts Which expression represent a half-angle identity for cosine, $\cos \dfrac{x}{2}?$
 $\cos \dfrac {x}{2}=\pm \sqrt{\dfrac{1-\cos x}{1+\cos x}}$ $\cos \dfrac {x}{2}=\pm \sqrt{\dfrac{1+\cos x}{2}}$
•  Question 3: 1 pts $$\sin 2x=2\sin x$$
•  Question 4: 1 pts $$\tan \dfrac{x}{2}\neq \dfrac{1}{2}\tan x$$
•  Question 5: 2 pts Use a double-angle identity to find the exact value of $\sin 120^{\circ}.$
 $1$ $\dfrac{\sqrt{3}}{3}$ $\dfrac{1}{2}$ $\dfrac{\sqrt{3}}{2}$
•  Question 6: 2 pts Simplify the expression. $$\left(\cos 5+\sin 5\right)^{2}$$
 $1+\sin 10$ $1+\cos 10$ $1-\sin 10$ $1-\cos 10$
•  Question 7: 2 pts If $\cos \theta=\dfrac{2\sqrt{5}}{5}$ and $0^{\circ}<\theta<90^{\circ}$ then find $\sin \dfrac{\theta}{2}.$
$\sin \dfrac{\theta}{2}=$
•  Question 8: 2 pts If $\cot\theta=-\dfrac{24}{7}$ and $\dfrac{3\pi}{2}<\theta<2\pi$ then find $\tan \dfrac {\theta}{2}.$
$\tan \dfrac {\theta}{2}=$
•  Question 9: 3 pts $$\sin 15^{\circ} \cos 15^{\circ}=\dfrac{1}{4}$$
•  Question 10: 3 pts $$\cot \dfrac{\pi}{8}-\tan\dfrac{\pi}{8}=1$$
•  Question 11: 3 pts Simplify the expression. $$\csc\alpha-\cot\alpha$$
 $\sin \dfrac{\alpha}{2}$ $\tan \dfrac{\alpha}{2}$ $\cos \dfrac{\alpha}{2}$ $\cot \dfrac{\alpha}{2}$