Question

Find the value:
$\frac{cos(90 + a)sec( - a)tan(180 - a)}{sec(360 - a)sin(180 - a)cot(90 - a)}$
​

Answer 1

$\sf{\underline{\boxed{\blue{\large{\bold{ Question}}}}}}$

• $\sf\dfrac{cos(90 + a)sec( - a)tan(180 - a)}{sec(360 - a)sin(180 - a)cot(90 - a)}$

$\sf{\underline{\boxed{\blue{\large{\bold{ Identities \:used }}}}}}$

$\sf{\bold{\green{\underline{\underline{\dag Cos( 90 + \theta ) = - sin \theta }}}}}$

$\sf{\bold{\green{\underline{\underline{\dag Sec( -\theta) = sec \theta}}}}}$

$\sf{\bold{\green{\underline{\underline{\dag tan( 180 - \theta ) = - cot \theta}}}}}$

$\sf{\bold{\green{\underline{\underline{\dag sec( 360 - \theta ) = sec \theta}}}}}$

$\sf{\bold{\green{\underline{\underline{\dag sin( 180 - \theta ) = cos \theta}}}}}$

$\sf{\bold{\green{\underline{\underline{\dag cot( 90 - \theta ) = tan \theta}}}}}$

$\sf{\bold{\green{\underline{\underline{\dag \dfrac{sin\theta}{cos\theta} = tan\theta}}}}}$

$\sf{\underline{\boxed{\blue {\large{\bold{ Solution}}}}}}$

$\sf\implies \dfrac{cos(90 + a)sec( - a)tan(180 - a)}{sec(360 - a)sin(180 - a)cot(90 - a)}$

$\sf\implies \dfrac{- sin \:a\times sec \: a\times - cot \: a }{sec\: a\times cos\: a \times tan\: a }$

$\sf\implies \dfrac{- sin \:a\times \cancel{sec a}\times - cot \: a }{\cancel{sec\: a}\times cos\: a \times tan\: a }$

$\sf\implies \dfrac{- sin \:a\times - cot \: a }{ cos\: a \times tan\: a }$

$\sf\implies \dfrac{- tan\: a \times - cot\: a}{tan\: a}$

$\sf\implies \dfrac{-\cancel{ tan\: a }\times - cot\: a}{\cancel{tan\: a}}$

$\sf\implies - ( - tan\:a)$

$\sf\implies tan\:a$

$\sf{\red{\boxed{\bold{\dag tan \: a}}}}$