Question

1. Show that sinA cosA tanA + cosA sinA cotA = 1.

Answer 1

Step-by-step explanation:

[ Refer to the attachment ]

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$\tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ \\ \cot( \alpha ) = \frac{ \cos( \alpha ) }{ \sin( \alpha ) }$

and the identity ;

Sin²x + cos²x = 1

Answer 2

$\large \bf \orange {Solution : }$

On Solving LHS

$\bf \Longrightarrow \sin a .\cos a. \tan a + \cos a. \sin a . \cot a \\ \\ \bf \Longrightarrow \sin a . \: \cancel{\cos a}. (\frac{ \sin a }{ \cancel{\cos a }} ) + \cos a. \cancel{\sin a }.( \frac{ \cos a }{ \cancel{\sin a} }) \\ \\ \bf \Longrightarrow { \sin }^{2} a + { \cos}^{2} a \\ \\ \bf \Longrightarrow 1$

Which is equal to RHS

Hence Proved