Prove thattan -sec -1-tan -sec -1-2 cosec - -4 MARKS-

Formula: 1 Mark Concept: 1 Mark Application: 2 Marks tan θ/sec θ 1+tan θ/sec θ+1 =tan θ(sec θ+1)+tan θ(sec θ 1)/sec^2 θ 1 =2 tan θ sec θ + tan θ tan θ/tan^2 ...

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Standard XII

Mathematics

Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

Prove thattan...

Question

Prove that

$\frac{t a n θ}{s e c θ - 1} + \frac{t a n θ}{s e c θ + 1} = 2 c o s e c θ$ [4 MARKS]

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Solution

Formula: 1 Mark
Concept: 1 Mark
Application: 2 Marks

$\frac{t a n θ}{s e c θ - 1} + \frac{t a n θ}{s e c θ + 1}$

$= \frac{t a n θ (s e c θ + 1) + t a n θ (s e c θ - 1)}{s e c^{2} θ - 1}$

$= \frac{2 t a n θ s e c θ + t a n θ - t a n θ}{t a n^{2} θ}$

$= \frac{2 t a n θ s e c θ}{t a n^{2} θ}$

$= \frac{2 \frac{1}{c o s θ}}{\frac{s i n θ}{c o s θ}}$

$= \frac{2}{s i n θ}$

$= 2 c o s e c θ$

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Prove that tan θsec θ−1+tan θsec θ+1=2 cosec θ [4 MARKS]

Formula: 1 Mark Concept: 1 Mark Application: 2 Marks tan θsec θ−1+tan θsec θ+1 =tan θ(sec θ+1)+tan θ(sec θ−1)sec2 θ−1 =2 tan θ sec θ+tan θ−tan θtan2 θ =2 tan θ sec θtan2 θ =21cos θsin θcos θ =2sin θ =2 cosec θ

Prove that

$\frac{t a n θ}{s e c θ - 1} + \frac{t a n θ}{s e c θ + 1} = 2 c o s e c θ$ [4 MARKS]