Prove that- sin- 1 - tan- - cos- 1 - - - - - cosec -

[ sinθ( 1 + tanθ) + cosθ( 1 + θ); = sinθ ...

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Trigonometric Identities

Prove that: ...

Question

Prove that: $sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + c o s e c θ$ .

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sin θ (1 + tan θ) + cos θ (1 + cot θ) = s e c θ + c o s e c θ

sin θ (1 + tan θ) + c o s θ (1 + cot θ) = csc θ + sec θ

\frac{sinθ}{(1 - cotθ)} + \frac{cosθ}{(1 - tanθ)} = ?

\frac{tan θ}{sec θ + 1} + \frac{cot θ}{c o s e c θ + 1} = c o s e c θ + sec θ - sec θ . c o s e c θ

\frac{\sin^{2} θ}{cosθ} + cosθ = secθ

\cos^{2} θ (1 + \tan^{2} θ) = 1

\sqrt{\frac{1 - sinθ}{1 + sinθ}} = secθ - tanθ

(secθ - cosθ) (cotθ + tanθ) = tanθ secθ

cotθ + tanθ = cosecθ secθ

\frac{1}{secθ - tanθ} = secθ + tanθ

\sec^{4} θ - \cos^{4} θ = 1 - 2 \cos^{2} θ

secθ + tanθ = \frac{\cos θ}{1 - sinθ}

t anθ + \frac{1}{tanθ} = 2

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\frac{tanA}{{(1 + \tan^{2} A)}^{2}} + \frac{cotA}{{(1 + \cot^{2} A)}^{2}} = \sin A \cos A

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\frac{tanθ}{secθ - 1} = \frac{tanθ + secθ + 1}{tanθ + secθ - 1}

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