Question

If cos e * c * A = 2 , find the value of: (sin 2A + cos 2A)/(tan A)​

Answer 1

Answer:

(3 + √3)/2

Step-by-step explanation:

cosecA = 2   ⇒ sinA = 1/2

                     ⇒ sinA = sin30°

                     ⇒ A = 30°

Hence, 2A = 2(30°)  ⇒ 2A = 60°

  Therefore,

⇒ (sin2A + cos2A)/tanA

⇒ (sin60°  + cos60°)/tan30°

⇒ (√3/2 + 1/2)/(1/√3)

⇒ (√3 + 1)/2 / (1/√3)

⇒ √3(√3 + 1)/2  or (3 + √3)/2

Answer 2

~Solution :-

$\sf{cosecA = 2}$

$\sf{⇒ sinA = 1/2 }$

$\sf{⇒ sinA = sin30°}$

Hence,

$\bf \red{⇒ A = 30°}$

So,

$\sf{ 2A = 2(30°)   \longrightarrow 2A = 60°}$

•   Therefore,

$\sf{⇒ \frac{(sin2A + cos2A)}{tanA }}$

$\sf{⇒ \frac{ (sin60°  + cos60°)}{tan30°}}$

$\sf{⇒ \frac{(\frac{ \sqrt3}{2} + \frac{1}{2})}{ (\frac{1}{ \sqrt3})}}$

$\bf \red{⇒ \frac{\sqrt3( \sqrt3 + 1)}{2}  }$