Question

Tan (pi/24).tan (3pi/24).tan (5pi/24).tan (7pi/24).tan (9pi/24).tan (11pi/24).tan (13pi/24)=​

Answer 1

Given: The trigonometric equation : Tan (pi/24).tan (3pi/24).tan (5pi/24).tan (7pi/24).tan (9pi/24).tan (11pi/24).tan (13pi/24)

To find: The value of given expression.

Solution:

• Now we have given :

              tan(π/24).tan (3π/24).tan (5π/24).tan (7π/24).tan(9π/24). tan(11π/24) .tan (13π/24)

• Now we know that tan x = cot(90 - x)

              So tan (π/24) = cot(90 - π/24) = cot(11π/24)

• Similarly:

              tan (3π/24) = cot (90 - 3π/24) = cot(9π/24)

• Similarly:

              tan (5π/24) = cot (90 - 5π/24) = cot(7π/24)

• Now substituting in given expression, we get:

              cot(11π/24) cot(9π/24).cot(7π/24).tan (7π/24).tan(9π/24).tan(11π/24). tan (13π/24)

• Rearranging the terms, we get:

              cot(11π/24)tan(11π/24) x  cot(9π/24)tan(9π/24) x cot(7π/24) tan(7π/24) x tan (13π/24)

• Now we know that ( tan x )( cot x ) = 1, so:

              1 x 1 x 1 x tan (13π/24)

              tan (13π/24)

Answer:

            So the final value comes out to be tan (13π/24)

Answer 2

Answer:

Hope it helps uuuu......