Question

(i) Solve
(i) tan 15⁰an 20°. tan 70°.tan 75°
=​

Answer 1

Answer

$\\ \sf\longmapsto tan15\times tan20\times tan70\times tan75$

$\\ \sf\longmapsto tan15\times tan75\times tan20\times tan70$

$\\ \sf\longmapsto tan(15+75)\times tan(20+70)$

$\\ \sf\longmapsto tan90\times tan90$

$\\ \sf\longmapsto 1\times 1$

$\\ \sf\longmapsto 1$

Answer 2

Answer :-

• Value of tan 15° tan 20° tan 70° tan 75° is 1.

Step-by-step explanation :-

Given :

• tan 15° tan 20° tan 70° tan 75°

To find :

• The simplified value.

Solution :

We know,

• tan(90° - θ) = cot θ

So,

⇒ tan 15° × tan 20° × cot (90° - 70°) × cot (90° - 75°)

⇒ tan 15° × tan 20° × cot 20° × cot 15°

⇒ (tan 15° × cot 15°) (tan 20° × cot 20°)

We know,

• tanθ.cotθ = 1

So,

⇒ 1 × 1

⇒ 1

∴ Value of tan 15° tan 20° tan 70° tan 75° is 1.