Evaluate tan2-2-2-2-cosec2-

According to question, tan^2θ+^2θ+2=^2θ+cosec^2θ ⇒ sec^2θ+cosec^2θ tan^2θ cot^2θ=2 LHS, #160; sec^2θ tan^2θ+cosec^2θ cot^2θ ⇒ 1+ ...

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Trigonometric Identities

Evaluate tan...

Question

Evaluate
${tan}^{2} θ + {cot}^{2} θ + 2 = {sec}^{2} θ + c o s e c^{2} θ$

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Solution

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s e c^{2} θ + c o s e c^{2} θ = s e c^{2} θ c o s e c^{2} θ

t a n^{2} θ - s i n^{2} θ = t a n^{2} θ s i n^{2} θ

t a n^{2} θ + c o t^{2} θ + 2 = s e c^{2} θ c o s e c^{2} θ

\frac{{cot}^{2} θ + {sec}^{2} θ}{{tan}^{2} θ + {cosec}^{2} θ} = (sin θ cos θ) (tan θ + cot θ)

\frac{{tan}^{2} θ}{{sec}^{2} θ} + \frac{{cot}^{2} θ}{c o s e c^{2} θ} = 1

tan θ = \frac{1}{\sqrt{3}}

\frac{cos e c^{2} θ - {sec}^{2} θ}{cos e c^{2} θ + {sec}^{2} θ}

{sin}^{2} θ + {cos}^{2} θ + {sec}^{2} θ + c o s e c^{2} θ + {tan}^{2} θ + {cot}^{2} θ

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