Question

If tan theta =20/21 , evaluate 1-sin theta +cos theta /1 +sin theta +cos theta.

Answer 1

HI !

tanθ = 20/21 = opposite side(o)/adjacent side(a)

hypotenuse = h = o² + a²

Let , o = 20k  and a = 21k

h² = (20k)² + (21k)²
   = 841k²

h = 29 k

sinθ = o/h 
        = 20k/29k
        =20/29

cosθ = a/h 
         = 21k/29k
        = 21/29

1 - sinθ + cosθ ÷ 1 + sinθ + cosθ

= {1 - 20/29 + 21/29 / 1 } ÷ {1 + 20/29 + 21/29}

= {29/29 - 20/29 + 21/29) ÷ {29/29+20/29+21/29}

= {29 - 20 + 21/29} ÷ {29+20+21/29}

= 30/29 ÷  70/29

29 gets cancelled on both denominator and numerator.

= 30/70

= 3/7

Answer 2

hope it help you .

@rajukumar ◆◆◆◆sorry for wrong answer.