Question

1-COS A
ii) sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A
sin A)
cos)
(cort​

Answer 1

✒️QUESTION✒️

$\small{ \sf \dag\sin A(1 + \tan A )+ \cos A(1 + \cot A ) = \sec A + \cosec A }$

✒️ANSWER✒️

☄️GIVEN☄️

$\small{ \sf \bull \sin A(1 + \tan A )+ \cos A(1 + \cot A ) = \sec A + \cosec A }$

☄️PROVE THAT☄️

$\sf{ \bull L.H.S = R.H.S}$

☄️PROOF☄️

L.H.S

$\sf ➔ \sin A(1 + \tan A )+ \cos A(1 + \cot A )$

$\sf ➔ \sin A + \sin A \tan A + \cos A + \cos A \cot A$

$\sf ➔ \sin A + \sin A \times \frac{ \sin A}{\cos A} + \cos A + \cos A \times \frac{\cos A}{\sin A}$

$\sf ➔ \sin A + \frac{{\cos}^2 A} { \sin A} + \cos A + \frac{{\sin} ^ 2A } {\cos A}$

$\sf ➔ \frac{ {\sin}^{2}A + {\cos}^2 A} { \sin A} + \frac{{\cos}^2 A + {\sin}^{2}A }{ \cos A }$

$\sf ➔ \frac{ 1} { \sin A} + \frac{1}{ \cos A } \: \: \: \: ( { \sin}^{2} A + { \cos}^{2} A = 1)$

$\sf = \cosec A + \sec A$

L.H.S = R.H.S

HENCE, PROVED.