Question

(seca-cosa).(cot a +tan a) = seca .tan a​

Answer 1

To prove:

(secA - cosA) (cotA + tanA) = secA × tanA

Proof:

= (secA - cosA) (cotA + tanA)

= $\rm (secA - \frac{1}{secA}) (\frac{1}{tanA} + tanA)$

Taking LCM

= $\rm (\frac{sec^2A - 1}{secA}) (\frac{1 + tan^2A} {tanA})$

= $\rm\frac{tan^2A}{secA} × \frac{sec^2A}{tanA}$

= secA × tanA

LHS = RHS

Hence Proved

IDENTITY USED:

1 + tan^2A = sec^2A

OR

tan^2A = sec^2A - 1