Question

tan(π÷ 24 )- tan( 5π÷24) + tan(7π÷24) - tan( 11 π÷ 24)

Answer 1

Answer:

Step-by-step explanation:

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:

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)

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

           

Answer 2

Answer:4/

Step-by-step explanation: