Question

The value of

\[\frac{\cos \left( 90°- \theta \right) \sec \left( 90°- \theta \right) \tan \theta}{cosec \left( 90°- \theta \right) \sin \left( 90° - \theta \right) \cot \left( 90°- \theta \right)} + \frac{\tan \left( 90° - \theta \right)}{\cot \theta}\] 

 

Options

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Answer 1

We have to find:  \[\frac{\cos \left( 90°- \theta \right) \sec \left( 90°- \theta \right) \tan \theta}{cosec \left( 90°- \theta \right) \sin \left( 90° - \theta \right) \cot \left( 90°- \theta \right)} + \frac{\tan \left( 90° - \theta \right)}{\cot \theta}\] 

so 

\[\frac{\cos \left( 90°- \theta \right) \sec \left( 90°- \theta \right) \tan \theta}{cosec \left( 90°- \theta \right) \sin \left( 90° - \theta \right) \cot \left( 90°- \theta \right)} + \frac{\tan \left( 90° - \theta \right)}{\cot \theta}\] 

= `(sin θ cosec θ tan θ) /(sec θ  cos θ  tan θ )+cot θ / cot θ ` 

=` (1 xx tan θ) /(1xx tan θ )+cot θ /cot θ ` 

=`1+1` 

=`2`