Question

secθ-1+tanθ/cosecθ- 1 + cotθ = cotθ


fast solution plz.​

Answer 1

Answer:

${ \huge{ \underline{ \bf{ \red{question}}}}}$

${ \sf{ \frac{sec θ- 1 + tanθ}{cosecθ - 1 + cotθ} = cot θ}}$

Solution:-

${ \to { \sf{\frac{sec</strong><strong>θ</strong><strong> - 1 + </strong><strong>tanθ</strong><strong>}{cosec </strong><strong>θ</strong><strong>- 1 + </strong><strong>cotθ</strong><strong>} }}}$

${ \to{ \sf{ \frac{ \frac{1}{cos</strong><strong>θ</strong><strong>} - 1 + \frac{sin</strong><strong>θ</strong><strong>}{cos</strong><strong>θ</strong><strong>} }{ \frac{1}{sin</strong><strong>θ</strong><strong>} - 1 + \frac{cos</strong><strong>θ</strong><strong>}{sin</strong><strong>θ</strong><strong>} } }}}$

${ \to{ \sf{ \frac{ \frac{1}{cos</strong><strong>θ</strong><strong>} - \frac{cos</strong><strong>θ</strong><strong> + </strong><strong>sinθ</strong><strong>}{</strong><strong>cosθ</strong><strong>} }{ \frac{1}{sin</strong><strong>θ</strong><strong>} - \frac{sin</strong><strong>θ</strong><strong> + </strong><strong>cosθ</strong><strong>}</strong><strong>{</strong><strong>sinθ</strong><strong>}</strong><strong>}</strong><strong> }}}$

${ \to{ \sf{ \frac{ \frac{1 - </strong><strong>cosθ</strong><strong> \: + </strong><strong>sinθ</strong><strong>}</strong><strong> {</strong><strong>cosθ</strong><strong>} }{ \frac{1 - </strong><strong>sinθ</strong><strong> + </strong><strong>cosθ</strong><strong>}{</strong><strong>sinθ</strong><strong>} } }}}$

${ \to{ \sf{ \frac{ \frac{{ \cancel{1 - </strong><strong>cosθ</strong><strong> + </strong><strong>sinθ</strong><strong>}}}{</strong><strong>cosθ</strong><strong>} }{ \frac{{ \cancel{1 - </strong><strong>sinθ</strong><strong> + </strong><strong>cosθ</strong><strong>}}}{</strong><strong>sinθ</strong><strong>} } }}}$

${ \to{ \sf{ \frac{cos</strong><strong>θ</strong><strong>}{sin</strong><strong>θ</strong><strong>} }}}$

${ \to{ \sf{cot</strong><strong>θ</strong><strong>}}}$

Therefore,

secθ-1+tanθ/cosecθ-1+cotθ=cotθ