Math, asked by AkshataTiwari, 1 year ago

cot theta upon cot theta minus Cot 3 theta + tan theta upon tan theta minus tan 3 theta is equal to

Answers

Answered by priyaanand29061979
131

Answer:

Step-by-step explanation:i have written the answers with the proper steps. Refer below

Attachments:
Answered by gratefuljarette
71

The value of \frac{\cot \theta}{\cot \theta-\cot 3 \theta}+\frac{\tan \theta}{\tan \theta-\tan 3 \theta} is 1

Given:

\frac{\cot \theta}{\cot \theta-\cot 3 \theta}+\frac{\tan \theta}{\tan \theta-\tan 3 \theta}

To find:

The value of \frac{\cot \theta}{\cot \theta-\cot 3 \theta}+\frac{\tan \theta}{\tan \theta-\tan 3 \theta}

Solution:

To simplify, \frac{\cot \theta}{\cot \theta-\cot 3 \theta}+\frac{\tan \theta}{\tan \theta-\tan 3 \theta}

Take LCM, the equation becomes,  

=\frac{[\cot \theta \times(\tan \theta-\tan 3 \theta)][\tan \theta \times(\cot \theta-\cot 3 \theta]}{(\cot \theta-\cot 3 \theta) \times(\tan \theta-\tan 3 \theta)}

=\frac{[\cot \theta \times(\tan \theta-\tan 3 \theta)][\tan \theta \times(\cot \theta-\cot 3 \theta]}{(\cot \theta \times \tan \theta)-(\cot 3 \theta \times \tan \theta)+(\cot \theta \times \tan \theta)-(\tan 3 \theta \times \cot \theta)}

Since \cot \theta \times \tan \theta=1

=\frac{1-(\cot \theta \times \tan 3 \theta)+1-(\tan \theta \times \cot 3 \theta)}{(1)-(\cot 3 \theta \times \tan \theta)+(1)-(\tan 3 \theta \times \cot \theta)}

=\frac{2-(\cot \theta \times \tan 3 \theta)-(\tan \theta \times \cot 3 \theta)}{(2)-(\cot 3 \theta \times \tan \theta)-(\tan 3 \theta \times \cot \theta)}

Since numerator and denominator are equal, \frac{\cot \theta}{\cot \theta-\cot 3 \theta}+\frac{\tan \theta}{\tan \theta-\tan 3 \theta}=1

Similar questions