If tan θ = 20/21 , show that 1-sin θ + cos θ/1+sin θ + cos θ = 3/7

Question

If tan θ = \(\frac{20}{21}\), show that \(\frac{1-sinθ + cos θ}{1+sinθ + cos θ}\) = \(\frac{3}7\)

Answer 1

Given: tan θ = \(\frac{20}{21}\)

Solution: Since tanθ = perpendicular / base

So, we construct a right triangle ABC right angled at C 

such that ∠ABC =θ and AC = Perpendicular = 20

BC = base = 21

By Pythagoras theorem,

AB² = AC² + BC² 

⇒ AB² = (20)² + (21)² 

⇒ AB² = 400 + 441 

⇒ AB² = 841 

⇒ AB = √841

⇒ AB = 29

As sinθ = perpendicular / hypotenusecosθ = base / hypotenuse So,

tan θ = \(\frac{20}{21}\)

⇒ sin θ = \(\frac{20}{29}\) and cos θ = \(\frac{21}{29}\)

Hence proved