Question

ம‌தி‌ப்புகளை‌க் கா‌ண்க

tan15°tan30°tan45°tan60°tan75°

Answer 1

Step-by-step explanation:

Let put every ratio in such a manner that the sum of ratio will be 90°

tan15° tan75° tan30° tan60° tan45

tan(90-75) tan75° tan(90-60) tan60° tan45

* [tan(90-A)=cotA]

So

cot75°tan75° cot60°tan60°tan45°

1/tan75°*tan75° 1/tan60°*tan60° tan45

1*1*1 "[cotA=1/tanA] [tan45°=1]"

So the solution to this is

1

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Answer 2

விளக்கம்:

tan 15° tan 30° tan 45° tan 60° tan 75°

⇒ tan 15° tan . tan 30° tan 45° tan 60°

$\tan \left(90^{\circ}-\theta\right)=\cot \theta$

⇒ tan 30° = $\frac{1}{\sqrt{3}}$

⇒ tan 45° = 1

$\Rightarrow \tan 60^{\circ}=\sqrt{3}$

$\tan \left(90^{\circ}-15^{\circ}\right)=\tan 75^{\circ}=\cot 15^{\circ}$

$\left(\tan 15^{\circ}\right)-\left(\cot 15^{\circ}\right)\left(\frac{1}{\sqrt{3}}\right) \cdot(1)(\sqrt{3})$

$\Rightarrow \tan 15^{\circ}\left(\frac{1}{\left.\tan 15^{\circ}\right)}\left(\frac{1}{\sqrt{3}}\right) \cdot(1)(\sqrt{3})\right.$

$\Rightarrow 1$

tan 15° tan 30° tan 45° tan 60° tan 75° ன் மதிப்பு 1 ஆகும்.