Question

Sin 12° + cos 12°/sin 12° - Cos12°

Answer 1

AnswEr :

To find the value of;

$\sf \: \dfrac{sin12 + cos12}{sin12 - cos12}$

Multiplying and dividing by sin12 + cos12.

$\longrightarrow \sf \: \dfrac{sin12 + cos12}{sin12 - cos12} \times \dfrac{sin12 + cos12}{sin12 + cos12} \\ \\ \longrightarrow \: \sf \: \dfrac{(sin12 + cos12) {}^{2} }{(sin12 + cos12)(sin12 - cos12)} \\ \\ \longrightarrow \: \sf \: \dfrac{ {sin}^{2}12 + cos {}^{2}12 + 2sin12.cos12 }{ {sin}^{2}12 - {cos}^{2} 12 } \\ \\ \longrightarrow \sf \: \dfrac{1 + sin2(12)}{ - \: cos2(12)} \\ \\ \longrightarrow \: \sf \: - \dfrac{1}{cos24} - \dfrac{sin24}{cos24} \\ \\ \longrightarrow \: \sf \: - (sec24 + tan24)$

Now,

• sec24 ≈ 2.36
• tan24 ≈ - 2.18

Thus,

$\longrightarrow \sf \: - (2.36 - 2.18) \\ \\ \longrightarrow \sf - 0.18$

The value of above expression is - 0.18

Identifies UseD :

• sin²∅ + cos²∅ = 1

• cos²∅ - sin²∅ = cos2∅

• 2sin∅cos∅ = sin2∅