Question

Prove that tan 15 Degree + cot 15 Degree = 4

Answer 1

Answer:

big proving that question I get answers 0

Answer 2

To ProvE :

tan 15°+ cot 15° = 4.

SolutioN :

$\tt : \implies tan \: 15 \degree + cot \: 15\degree.$

$\tt : \implies \dfrac{sin \: 15 \degree }{cos \: 15 \degree}+ \dfrac{cos 15\degree.}{sin \: 15 \degree}$

★ Taking LCM.

$\tt : \implies \dfrac{{sin}^{2} 15 \degree +{ cos }^{2} 15\degree}{sin \: 15 \degree.cos \: 15 \degree}$

★ We know,

• Sin²A + Cos²A = 1.

$\tt : \implies \dfrac{1}{sin \: 15 \degree.cos \: 15 \degree}$

$\tt : \implies \dfrac{1}{ \dfrac{1}{2} sin \: 30\degree}$

$\tt : \implies \dfrac{1 \times 2}{ sin \: 30\degree}$

★ We can Write as Sin 30° → π/6.

$\tt : \implies \dfrac{2}{ sin \: \frac{ \pi}{6} }$

$\tt : \implies 4.$

# Hence Proved.