Question

IOf $tan\theta=\frac{20}{21}$, then the Value of $\frac{Sin{\theta}-Cos{\theta}}{Sin{\theta}+Cos{\theta}}$

• A. $$\frac{-1}{41}$$
• B. $$\frac{29}{35}$$
• C. $$\frac{27}{21}$$
• D. $$\frac{-29}{31}$$

Answer 1

Answer:

$$\frac{-1}{41}$$

Solution: Given: tan θ = 20/21 Formula: If x/y = a/b, then Dividendo and Componendo (x + y)/(x - y) = (a + b)/(a - b) Calculation: tan θ = 20/21 ⇒ sin θ/cosθ = 20/21 Dividendo and Componendo ⇒ (sin θ + cos θ)/(sin θ - cos θ) = (20 + 21)/(20 - 21) ⇒ (sin θ + cos θ)/(sin θ - cos θ) = 41/(-1) ∴ (sin θ - cos θ)/(sin θ + cos θ) = -1/41