It's trigo time #9

Geometry Level 2

$\large \frac{\sin\theta + \sin2\theta }{1+\cos\theta +\cos2\theta} = \ ?$

Prove your answer.

This is a part of the set It's trigo time .

\cot\theta

\cos\theta

\tan\theta

\sin^2\theta

2 solutions

Syed Hamza Khalid
May 19, 2017

This solution might be too long because it is very step by step answer. Very useful for beginners to trigonometric identities.

Chew-Seong Cheong
May 18, 2017

$\begin{aligned} \frac {\sin \theta+\sin 2\theta}{1+\cos \theta + \cos 2\theta} & = \frac {\sin \theta + 2\sin \theta \cos \theta}{1+\cos \theta +2\cos^2 \theta - 1} \\ & = \frac {\sin \theta (1+2\cos \theta)}{\cos \theta (1+2\cos \theta)} \\ & = \frac {\sin \theta}{\cos \theta} \\ & = \boxed{\tan \theta} \end{aligned}$

Thanks. A really good solution. very helpful. check out these as well:

https://brilliant.org/problems/its-trigo-time-10/

https://brilliant.org/problems/its-trigo-time-11/

Syed Hamza Khalid - 4 years ago

Thanks. You should use \ [ \ ] instead of \ ( ) then the formulas will turn out well. Also put a backslash \ before all functions such as \sin x (\sin x), \cos x $\cos x$ , \tan x $\tan x$ , \sec x $\sec x$ , \cot x $\cot x$ , \csc x $\csc x$ . Notice the text is not italic and there is a space between the function and x. Notice without backslash, sin x $sin x$ , cos x $cos x$ , tan x $tan x$ , sec x $sec x$ , cot x $cot x$ , csc x $csc x$ .

Chew-Seong Cheong - 4 years ago

Ok. Thanks a lot for your advice

Syed Hamza Khalid - 4 years ago

It's trigo time #9

2 solutions

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