Question

♠ Find the value of :
→ tan 15°​

Answer 1

$\huge\sf{\underline{\underline{\orange{Solution}}}}$

⇨ $\bf{tan 15° = tan(60° - tan45°)}$

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⇨ $\bf{tan 15° = \dfrac{tan 60° - tan 45°}{1 + tan 60° × tan 45°}}$

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⇨ $\bf{tan 15° = \dfrac{\sqrt{3} - 1}{1 + \sqrt{3}}}$

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$\large\mathcal{\underline{\green{Rationalising}}}$

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⇨ $\bf{\dfrac{\sqrt{3} - 1}{1 + \sqrt{3}} × \dfrac{\sqrt{3} - 1}{\sqrt{3} - 1}}$

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⇨ $\bf{\dfrac{(\sqrt{3})^2 + (1)^2 - 2\sqrt{3}}{3 - 1}}$

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⇨ $\bf{\dfrac{4 - 2\sqrt{3}}{2}}$

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$\large{\boxed{\purple{2 - \sqrt{3}}}}$

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★ $\large\sf{\underline{\pink{Value}}}$

✒ $\bf{tan 60° = \sqrt{3}}$

✒ $\bf{tan 45° = 1 }$

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★ $\large\sf{\underline{\pink{Formula\: used}}}$

✒ $\bf{tan(A - B) = \dfrac{tanA - tanB}{1 + tanA.tanB}}$

Answer 2

Answer:

Tan (15°) can be found if we know the value of sin 15 degrees and cos 15 degrees. ...

From the above table, we have the values of tan, sin and cos ratios for 0°, 30°, 45°, 60° and 90°. ...

tan (15°) = √3 – 1/ √3 + 1.

Hence, the value of tan (15°) is √3 – 1/√3 + 1.

∴ Tan (15°) = (1.732 – 1)/(1.732 + 1) = 0.2679.

Step-by-step explanation:

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