Question

if theta=π/4n, then find the value of tan theta, tan 2theta..............tan(2n-1)theta​

Answer 1

Answer:

Tan(π/4n) * Tan(2π/4n) * Tan(3π/4n) *.........Tan((2n-2)π/4n)*Tan((2n-1)π/4n)  = 1

Step-by-step explanation:

if theta=π/4n, then find the value of tan theta, tan 2theta..............tan(2n-1)theta​

Tan(π/4n) * Tan(2π/4n) * Tan(3π/4n) *............... Tan((2n-2)π/4n)*Tan((2n-1)π/4n)

Tan((2n-1)π/4n)  = Tan( 2nπ/4n - π/4n) = Tan(π/2 - π/4n) = 1/Tan(π/4n)

Tan((2n-2)π/4n)  = Tan( 2nπ/4n - 2π/4n) = Tan(π/2 - 2π/4n) = 1/Tan(2π/4n)

= Tan(π/4n) * Tan(2π/4n) * .....*Tan(nπ/4n)*.................*(1/Tan(2π/4n)*(1/Tan(π/4n)

= 1 * 1 * 1 *............* Tan(π/4)

= 1 * 1 * 1 *............* 1

= 1

Tan(π/4n) * Tan(2π/4n) * .........Tan((2n-2)π/4n)*Tan((2n-1)π/4n)  = 1

Answer 2

Answer:

1

Step-by-step explanation:

if theta=π/4n, then find the value of tan theta, tan 2theta..............tan(2n-1)theta​

Tan(π/4n) * Tan(2π/4n) * Tan(3π/4n) *............... Tan((2n-2)π/4n)*Tan((2n-1)π/4n)

Tan((2n-1)π/4n)  = Tan( 2nπ/4n - π/4n) = Tan(π/2 - π/4n) = 1/Tan(π/4n)

Tan((2n-2)π/4n)  = Tan( 2nπ/4n - 2π/4n) = Tan(π/2 - 2π/4n) = 1/Tan(2π/4n)

= Tan(π/4n) * Tan(2π/4n) * .....*Tan(nπ/4n)*.................*(1/Tan(2π/4n)*(1/Tan(π/4n)

= 1 * 1 * 1 *............* Tan(π/4)

= 1 * 1 * 1 *............* 1

= 1

Tan(π/4n) * Tan(2π/4n) * .........Tan((2n-2)π/4n)*Tan((2n-1)π/4n)  = 1