Question

Sin theta+ cos theta÷2 tan theta=

Answer 1

The final answer is " $\cot^2 \theta+ 2 \cot \theta\cos^2 \theta$"

Step-by-step explanation:

$\ Given \ value:\\\\\sin \theta+ \cos \theta \div \tan \theta= ?\\\\\ Find:\\\\value= ?\\\\\ Solution:\\\\\frac{\sin \theta+ \cos \theta}{\tan \theta} = ?\\\\\ square \ the \ above \ equation \\\\\rightarrow (\frac{\sin \theta+ \cos \theta}{\tan \theta})^2 \\\\\rightarrow \frac{(\sin \theta+ \cos \theta)^2}{\tan^2 \theta} \\\\\rightarrow \frac{(\sin^2 \theta+ \cos^2 \theta + 2 \sin \theta \cos \theta) }{\tan^2 \theta} \\\\\rightarrow \frac{(1 + 2 \sin \theta \cos \theta) }{\tan^2 \theta}$

$\rightarrow \frac{1}{\tan^2 \theta} + \frac{2 \sin \theta \cos \theta}{\tan^2 \theta} \\\\\rightarrow \cot^2 \theta+ \frac{2 \sin \theta \cos \theta}{\frac{\sin^2\theta}{\cos^2 \theta}} \\\\\rightarrow \cot^2 \theta+ \frac{2 \sin \theta \cos \theta \times \cos^2 \theta}{\sin^2\theta} \\\\\rightarrow \cot^2 \theta+ 2 \cot \theta\cos^2 \theta$

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