Question

Value of tan 15°. tn 45° tan 75° is

Answer 1

Step-by-step explanation:

tan15°×tan45°×tan75°

tan15°.tan45°.tan (90°-15°)

tan15°.tan45°.cot 15°[{{{cot×tan=1)))))

tan15°×cot15°×tan45°

1×tan45°(tan45°=1)

1×1=1

Answer 2

value of tan 15°. tan 45° .tan 75° is 1

Given:

• tan 15°. tan 45° .tan 75°

To Find:

• Value

Solution

• tan (90° - x) = cotx
• cot (90° - x) = tanx
• tanx = 1/cotx
• tanx.cotx  = 1
• tan 45°  = 1

tan 15°. tan 45° .tan 75°

Step 1:

Rewrite 75°  as 90° - 15°

tan 15°. tan 45° .tan (90° -15°)

Step 2:

Use identity tan (90° - x) = cotx

tan 15°. tan 45° .cot 15°

= tan 15°.cot 15°. tan 45°

Step 3:

Use identity tanx.cotx  = 1  and substitute  tan 45° = 1

1(1)

= 1

Hence, value of tan 15°. tan 45° .tan 75° is 1