Question

√1- cos theta/1+cos theta = cosec theta - cot theta​

Answer 1

Step-by-step explanation:

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Answer 2

Topic:-

Trigonometry

Question:-

$prove \: that \: \frac{ \sqrt{1 - cos \theta} }{1 + cos \theta} = csc \theta - cot \theta$

Solution:-

$take \: lhs \\ \\ \frac{ \sqrt{1 - cos \theta} }{ \sqrt{ 1 + cos \theta}} \\ \\ = \sqrt{ \frac{1 -cos \theta }{1 + cos \theta} } \times \sqrt{ \frac{1 - cos \theta}{1 - cos \theta} } \\ \\ = \sqrt{ \frac{(1 - cos \theta {)}^{2} }{1 - {cos}^{2} \theta } } \\ \\ = \sqrt{ \frac{(1 - cos \theta {)}^{2} }{ {sin}^{2} \theta} } \\ \\ = \frac{ \sqrt{(1 - cos \theta {)}^{2} } }{ \sqrt{ {sin}^{2} \theta} } \\ \\ = \frac{1 - cos \theta}{sin \theta} \\ \\ = \frac{1}{sin \theta} - \frac{cos \theta}{sin \theta} \\ \\ = csc \theta - cot \theta$

Hence Proved//:

More Information:-

Trigon metric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonmetric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj