Find the value of $$\tan{15^o} + \cot{15^o}$$​​

Correct option is A

To find: 

​cot15° + tan15°

Formula used:

​$$Sin^2\theta + Cos^2\theta = 1\\[5pt]tan\theta= \frac{sin\theta}{cos\theta},\\[5pt] Cot\theta= \frac{cos\theta}{sin\theta}\\[5pt]Sin2\theta = 2 sin\theta cos\theta$$​​

Solution:

​cot15° + tan15°

=> (cos15°/sin15°) + (sin15°/cos15°)

=> $$\frac{(cos^215° + sin^2 15°)}{(sin15° cos 15°)}$$​   (Sin²θ + cos²θ = 1)

=> $$\frac{1}{(sin15° cos15°)}$$​​

Multiply and divide equation by 2

=> $$\frac{2}{(2 sin15° cos15°)}$$​    (2 sinθ cosθ = sin2θ)

=> $$\frac{2}{sin30°}$$​     (sin30° = 1/2)

=> (2/1/2) = 2 × 2

=> 4

Hence, option (a) is the correct answer.