Best solutions to - "Establish identity 1−cos2θ1+sin⁡θ=sin⁡θ"

boitshupoO

Answered question

2021-09-06

Establish identity

1 - \frac{\cos^{2} θ}{1 + \sin θ} = \sin θ

Alannej

Skilled2021-09-07Added 104 answers

Given identity

1 - \frac{\cos^{2} θ}{1 + \sin θ} = \sin θ

First from the left-hand side,

1 - \frac{\cos^{2} θ}{1 + \sin θ}

Here use the Pythagorean trigonometry identity,

\cos^{2} θ = 1 - \sin^{2} θ

1 - \frac{\cos^{2} θ}{1 + \sin^{2} θ} = 1 - \frac{1 - \sin^{2} θ}{1 + \sin θ}

= 1 - \frac{(1 - \sin θ) (1 + \sin θ)}{(1 + \sin θ)}

= 1 - (1 - \sin θ)

= 1 - 1 + \sin θ

= \sin θ

Therefore it is established that the left-hand side equal to the right-hand side quantity

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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