Question

(Sec A - cos A) ( cot A + tan A) =tan A×sec A

Answer 1

Answer:

LHS = (1/cos A -cos A) (cosA/sinA + sin A/cos A)

= (1 - cos^2A/cos A) (cos^2A + sin^2A/sinAcosA)

= (sin^2A/cosA) ( 1 / sinAcosA)

= sin^2A/sinAcos^2A

= tanA x secA

Answer 2

Step-by-step explanation:

$\mathfrak{ \large \bold \blue{ \underline{ \underline{question}}}} \\ \implies{ \large{( \sec(a) - \cos(a) )( \cot(a) + \tan(a) = \tan(a) \times \sec(a) ) }} \\ \\ { \large \bold \orange{ \underline{solution}}} \\ \implies{ \large{( \sec(a) - \cos(a) )( \cot(a) + \tan(a) = \tan(a) \times \sec(a) ) }} \\ \implies{ \large{( \frac{1}{ \cos(a) } - \cos(a) )( \frac{ \cos(a) }{ \sin(a) } + \frac{ \sin(a) }{ \cos(a) } )}} \\ \implies{ \large{ \frac{1 - { \cos {}^{2} (a) }^{} }{ \cos(a) } \times \frac{ \cos {}^{2} (a) + \sin {}^{2} (a) }{ \cos(a) \times \sin(a) } }} \\ \implies{ \large{ \frac{ \sin {}^{2} (a) }{ \cos(a) } \times \frac{1}{ \cos(a) \sin(a) } }} \\ \implies{ \large{ \frac{ \sin(a) }{ \cos(a) } \times \frac{1}{ \cos(a) } }} \\ \implies{ \large{ \tan(a) \times \sec(a) }} \\ \\ { \large \bold \red{ \underline{hence \: proved}}}$