Question

if 1-sin theta+cos theta / 1+sin theta +cos theta = 3/7
prove that tan theta =20/21

Answer 1

Answer:

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

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

= RHS

Proved.

Answer 2

Answer:

I have attached above the solution

hope it helps

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