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The expresion \frac{tan A}{1-cotA}+\frac{cot A}{1-tan A}   can be written as :

 

 

 

 

 

  • Option 1)

    secA+cosecA

  • Option 2)

    sinA\, cos A+1

  • Option 3)

    secA\, cosecA+1

  • Option 4)

    tanA+cotA

 

Answers (1)

As we learnt in 

Trigonometric Ratios of Functions -

\sin \Theta = \frac{Opp}{Hyp}

\cos \Theta = \frac{Base}{Hyp}

\tan \Theta = \frac{Opp}{Base}

- wherein

Trigonometric Ratios of Functions

 

 

\frac{\tan A }{1-\cot A } + \frac{\cot A}{1 - \tan A}

 

\frac{\sin ^{2}A}{\cos A \left ( \sin A-\cos A \right )} - \frac{\left ( \\cos ^{2}{A} \right )}{ \left ( \sin A-\cos A \right )} \times \frac{1}{\sin A}

=\frac{\sin ^{3}A-\cos ^{3}A}{\left ( \sin A\cos A \right ) \: \left ( \sin A-\cos A \right )}

= \frac{\sin ^{2}A+\cos ^{2}A+\sin A\cos A}{\sin A\cos A}

= \frac{1+\sin A\cos A}{\sin A\cos A} = \sec A\ cosec\ A+1

 


Option 1)

secA+cosecA

Incorrect

Option 2)

sinA\, cos A+1

Incorrect

Option 3)

secA\, cosecA+1

Correct

Option 4)

tanA+cotA

Incorrect

Posted by

Sabhrant Ambastha

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