Prove that- 2 - - 1sin2 - - -1-

^2θ 1sin^2θ= 1 R.H.S. ^2θ 1sin^2θ =^2θ cosec^2θ = (cosec^2θ cot^2θ) = (1) = 1 = R.H.S. ...

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Trigonometric Identities

Prove that: ...

Question

Prove that: ${cot}^{2} θ - \frac{1}{{sin}^{2} θ} = - 1$ .

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{cot}^{2} θ - \frac{1}{{sin}^{2} θ} = - 1

\sqrt{\frac{1 + {sin}^{2} θ \cdot {sec}^{2} θ}{1 + {cos}^{2} θ \cdot {cosec}^{2} θ}} = tan θ

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

(sin θ + csc θ)^{2} = {sin}^{2} θ + {csc}^{2} θ + 2

{cos}^{4} θ - {sin}^{4} θ = 1 - 2 {sin}^{2} θ

(1 + {tan}^{2} θ) (1 + {cot}^{2} θ) = \frac{1}{({sin}^{2} θ - {sin}^{4} θ)}

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