The value of tan -16 - 2 tan -8 - 4 is equal to

The correct option is A π16 Using tan A = cot A #8211; 2 cot 2A we have LHS #160; ( 2A = ^2A 12 A) =( π16 22π16) + 2( π8 4π4) + ...

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Sum of Trigonometric Ratios in Terms of Their Product

The value of ...

Question

The value of tan $\frac{π}{16} + 2 tan \frac{π}{8} + 4$ is equal to

cot \frac{π}{8}

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cot \frac{π}{16}

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cot \frac{π}{16} - 4

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None of these

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Solution

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cot \frac{π}{32} - tan \frac{π}{32} - 2 tan \frac{π}{16} - 4 tan \frac{π}{8} =

{(\frac{x}{cos θ} + \frac{1}{x sin θ})}^{16}

l_{1}

x

\frac{π}{8} \leq θ \leq \frac{π}{4}

l_{2}

x

\frac{π}{16} \leq θ \leq \frac{π}{8},

l_{2} : l_{1}

y \leq \sqrt{16 - x^{2}}

∣ ∣ t a n^{- 1} (\frac{y}{x}) ∣ ∣ \leq \frac{π}{3}

p (x, y, x > 0

y \leq \sqrt{16 - x^{2}} a n d ∣ ∣ t a n^{- 1} (\frac{y}{x}) ∣ ∣ \leq \frac{π}{3}

l i m x \to \frac{π}{4} \frac{\int_{2}^{s e c^{2} x} f (t) d t}{x^{2} - \frac{π^{2}}{16}}

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