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Use Half-Angle Formulas To Rewrite Trigonometric Functions

Use half-angle formulas to rewrite $\frac{\left(1+\cos x\right)}{\sin x}$

$\cot\left(\frac{x}{2}\right)$

$\csc\left(\frac{x}{2}\right)$

$\tan\left(\frac{x}{2}\right)$

Use half-angle formulas to rewrite $\frac{\left(4-4\cos x\right)}{1+\cos x}$

$\frac{x}{2}$

$\frac{\sin x}{1+\cos x}$

$\frac{4x}{2}$

Use half-angle formulas to rewrite $\frac{\left(1-\cos x\right)}{\left(1+\cos x\right)}$

$\frac{x}{2}$

$\frac{\sin x}{1+\cos x}$

$\frac{3x}{2}$

Use half-angle formulas to rewrite $\tan\tan\ \left(\frac{x}{2}\right)$

$2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{\left(1-\cos x\right)}{\sin x}$

$\cos\left(\frac{x}{2}\right)$

Use half-angle formulas to rewrite $\frac{\left(1+\cos x\right)}{4}$

$2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{1}{2}\left(\frac{x}{2}\right)$

$\frac{x}{2}$

Use half-angle formulas to rewrite $\frac{\left(1+\cos x\right)}{2}$

$2\ \sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{\sin x}{1+\cos x}$

$\frac{x}{2}$

Use half-angle formulas to rewrite $\frac{\left(1-\cos x\right)}{2}$

$2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{\sin x}{1+\cos x}$

$\frac{x}{2}$

Use half-angle formulas to rewrite $2\left(1-\cos x\right)$

$\frac{x}{2}$

$\frac{\sin x}{1+\cos x}$

$\frac{3x}{2}$

Use half-angle formulas to rewrite $\frac{\left(1-\cos x\right)}{\sin x}$

$\tan\left(\frac{x}{2}\right)$

$\sin\left(x\right).\tan\left(\frac{x}{2}\right)$

$\frac{1}{\tan\left(\frac{x}{2}\right)}$

Use half-angle formulas to rewrite $\tan\tan\ \left(\frac{x}{2}\right)$

$2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{\left(\sin x\right)}{1+\cos x}$

$\cos\left(\frac{x}{2}\right)$

Questions

Time

Score

Use Half-Angle Formulas To Rewrite Trigonometric Functions

Use half-angle formulas to rewrite ﻿(1+cos⁡x)sin⁡x\frac{\left(1+\cos x\right)}{\sin x}sinx(1+cosx)​﻿

﻿cot⁡(x2)\cot\left(\frac{x}{2}\right)cot(2x​)﻿

﻿csc⁡(x2)\csc\left(\frac{x}{2}\right)csc(2x​)﻿

﻿tan⁡(x2)\tan\left(\frac{x}{2}\right)tan(2x​)﻿

Use half-angle formulas to rewrite ﻿(4−4cos⁡x)1+cos⁡x\frac{\left(4-4\cos x\right)}{1+\cos x}1+cosx(4−4cosx)​﻿

﻿x2\frac{x}{2}2x​﻿

﻿sin⁡x1+cos⁡x\frac{\sin x}{1+\cos x}1+cosxsinx​﻿

﻿4x2\frac{4x}{2}24x​﻿

Use half-angle formulas to rewrite ﻿(1−cos⁡x)(1+cos⁡x)\frac{\left(1-\cos x\right)}{\left(1+\cos x\right)}(1+cosx)(1−cosx)​﻿

﻿x2\frac{x}{2}2x​﻿

﻿sin⁡x1+cos⁡x\frac{\sin x}{1+\cos x}1+cosxsinx​﻿

﻿3x2\frac{3x}{2}23x​﻿

Use half-angle formulas to rewrite ﻿tan⁡tan⁡ (x2)\tan\tan\ \left(\frac{x}{2}\right)tantan (2x​)﻿

﻿2sin⁡(x2)cos⁡(x2)2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)2sin(2x​)cos(2x​)﻿

﻿(1−cos⁡x)sin⁡x\frac{\left(1-\cos x\right)}{\sin x}sinx(1−cosx)​﻿

﻿cos⁡(x2)\cos\left(\frac{x}{2}\right)cos(2x​)﻿

Use half-angle formulas to rewrite ﻿(1+cos⁡x)4\frac{\left(1+\cos x\right)}{4}4(1+cosx)​﻿

﻿2sin⁡(x2)cos⁡(x2)2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)2sin(2x​)cos(2x​)﻿

﻿12(x2)\frac{1}{2}\left(\frac{x}{2}\right)21​(2x​)﻿

﻿x2\frac{x}{2}2x​﻿

Use half-angle formulas to rewrite ﻿(1+cos⁡x)2\frac{\left(1+\cos x\right)}{2}2(1+cosx)​﻿

﻿2 sin⁡(x2)cos⁡(x2)2\ \sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)2 sin(2x​)cos(2x​)﻿

﻿sin⁡x1+cos⁡x\frac{\sin x}{1+\cos x}1+cosxsinx​﻿

﻿x2\frac{x}{2}2x​﻿

Use half-angle formulas to rewrite ﻿(1−cos⁡x)2\frac{\left(1-\cos x\right)}{2}2(1−cosx)​﻿

﻿2sin⁡(x2)cos⁡(x2)2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)2sin(2x​)cos(2x​)﻿

﻿sin⁡x1+cos⁡x\frac{\sin x}{1+\cos x}1+cosxsinx​﻿

﻿x2\frac{x}{2}2x​﻿

Use half-angle formulas to rewrite ﻿2(1−cos⁡x)2\left(1-\cos x\right)2(1−cosx)﻿

﻿x2\frac{x}{2}2x​﻿

﻿sin⁡x1+cos⁡x\frac{\sin x}{1+\cos x}1+cosxsinx​﻿

﻿3x2\frac{3x}{2}23x​﻿

Use half-angle formulas to rewrite ﻿(1−cos⁡x)sin⁡x\frac{\left(1-\cos x\right)}{\sin x}sinx(1−cosx)​﻿

﻿tan⁡(x2)\tan\left(\frac{x}{2}\right)tan(2x​)﻿

﻿sin⁡(x).tan⁡(x2)\sin\left(x\right).\tan\left(\frac{x}{2}\right)sin(x).tan(2x​)﻿

﻿1tan⁡(x2)\frac{1}{\tan\left(\frac{x}{2}\right)}tan(2x​)1​﻿

Use half-angle formulas to rewrite ﻿tan⁡tan⁡ (x2)\tan\tan\ \left(\frac{x}{2}\right)tantan (2x​)﻿

﻿2sin⁡(x2)cos⁡(x2)2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)2sin(2x​)cos(2x​)﻿

﻿(sin⁡x)1+cos⁡x\frac{\left(\sin x\right)}{1+\cos x}1+cosx(sinx)​﻿

﻿cos⁡(x2)\cos\left(\frac{x}{2}\right)cos(2x​)﻿

Incorrect

Great!

Use half-angle formulas to rewrite $\frac{\left(1+\cos x\right)}{\sin x}$

$\cot\left(\frac{x}{2}\right)$

$\csc\left(\frac{x}{2}\right)$

$\tan\left(\frac{x}{2}\right)$

Use half-angle formulas to rewrite $\frac{\left(4-4\cos x\right)}{1+\cos x}$

$\frac{x}{2}$

$\frac{\sin x}{1+\cos x}$

$\frac{4x}{2}$

Use half-angle formulas to rewrite $\frac{\left(1-\cos x\right)}{\left(1+\cos x\right)}$

$\frac{x}{2}$

$\frac{\sin x}{1+\cos x}$

$\frac{3x}{2}$

Use half-angle formulas to rewrite $\tan\tan\ \left(\frac{x}{2}\right)$

$2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{\left(1-\cos x\right)}{\sin x}$

$\cos\left(\frac{x}{2}\right)$

Use half-angle formulas to rewrite $\frac{\left(1+\cos x\right)}{4}$

$2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{1}{2}\left(\frac{x}{2}\right)$

$\frac{x}{2}$

Use half-angle formulas to rewrite $\frac{\left(1+\cos x\right)}{2}$

$2\ \sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{\sin x}{1+\cos x}$

$\frac{x}{2}$

Use half-angle formulas to rewrite $\frac{\left(1-\cos x\right)}{2}$

$2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{\sin x}{1+\cos x}$

$\frac{x}{2}$

Use half-angle formulas to rewrite $2\left(1-\cos x\right)$

$\frac{x}{2}$

$\frac{\sin x}{1+\cos x}$

$\frac{3x}{2}$

Use half-angle formulas to rewrite $\frac{\left(1-\cos x\right)}{\sin x}$

$\tan\left(\frac{x}{2}\right)$

$\sin\left(x\right).\tan\left(\frac{x}{2}\right)$

$\frac{1}{\tan\left(\frac{x}{2}\right)}$

Use half-angle formulas to rewrite $\tan\tan\ \left(\frac{x}{2}\right)$

$2\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

$\frac{\left(\sin x\right)}{1+\cos x}$

$\cos\left(\frac{x}{2}\right)$