Question

prove that: (sin + tan ) / sin = 1+ sec​

Answer 1

Answer:

Step-by-step explanation:

$\frac{sin A+tan A}{sinA}$

= $\frac{sin A}{sin A} + \frac{sin A}{cos A* sin A}$

= 1+1/cos A

=1+sec A

Answer 2

$\bullet\quad\rm \dfrac{sin + tan}{sin} = 1+sec$

• Multiply both the sides by sin

$\rm \dashrightarrow sin + tan=sin( 1+sec)$

$\rm \dashrightarrow sin + tan=sin+sin(sec)$

• Write sec as 1/cos .

$\rm \dashrightarrow sin + tan=sin+sin\Bigg (\dfrac{1}{cos}\Bigg )$

$\rm \dashrightarrow sin + tan=sin+\dfrac{sin}{cos}$

• sin/cos = tan

$\bf \dashrightarrow sin + tan=sin+tan$

Hence, Proved.