Question

Prove that : $( 1 + tan^{2} A) ( cos A * sin A) = tan A$

Answer 1

Ans

=> sec²A*cosA*sinA    (since, sec²A=1+tan²A)
=>(1/cos²A)*cosA*sinA  (since, secA=1/cosA)
=>sinA/cosA
=>tanA.     [proved]

Answer 2

Here's your answer!

$= > (1 + {tan}^{2} A)(cos \: A \times sin \: A) = tan \: A$

$= > ({sec}^{2} A)(cos \: A \times \: sin \: A) \: = tan \: A$

$= > (\frac{1}{ {cos}^{2} A})(cos \: A \times sin \: A) = tan \: A$

$= > \frac{sin \: A}{cos \: A} = tan \: A$

=> tan A = tan A

=> L.H.S = R.H.S

Hope it helps!