If \(\cot x = \dfrac{5}{12}\) , then sin x + cos x = ?A. \(\dfrac{31

1.	If \(\cot x = \dfrac{5}{12}\) , then sin x + cos x = ?A. \(\dfrac{31}{17}\)B. \(\dfrac{27}{13}\)C. \(\dfrac{13}{17}\)D. \(\dfrac{17}{13}\) 1. B2. D3. C4. A
Answer» Correct Answer - Option 2 : D Given: Cotx = 5/12 Formula used: Using basic trigonometric functions. 1) Cotx = B/P 2) Sinx = P/H 3) Cosx = B/H Where B is base, P is perpendicular and H is the hypotenuse Calculation: Cotx = 5/12 = B/P H² = B² + P² ⇒ H² = 5² + 12² = 25 + 144 ⇒ H² = 169 ⇒ H = 13 Sinx + Cosx = P/H + B/H = 12/13 + 5/13 ∴ Sinx + Cosx is 17/13

If \(\cot x = \dfrac{5}{12}\) , then sin x + cos x = ?A. \(\dfrac{31}{17}\)B. \(\dfrac{27}{13}\)C. \(\dfrac{13}{17}\)D. \(\dfrac{17}{13}\) 1. B2. D3. C4. A

Answer» Correct Answer - Option 2 : D

Given:

Cotx = 5/12

Formula used:

Using basic trigonometric functions.

1) Cotx = B/P

2) Sinx = P/H

3) Cosx = B/H

Where B is base, P is perpendicular and H is the hypotenuse

Calculation:

Cotx = 5/12 = B/P

H² = B² + P²

⇒ H² = 5² + 12² = 25 + 144

⇒ H² = 169

⇒ H = 13

Sinx + Cosx = P/H + B/H = 12/13 + 5/13

∴ Sinx + Cosx is 17/13