Question

Tan pi/20 tan 3pi/20 tan 5pi/20 tan 7pi/20 tan 9pi/20=​

Answer 1

Answer:

1

Step-by-step explanation:

tan(π/20) tan(3π/20) tan(5π/20) tan(7π/20) tan(9π/20) = 1.

To this end:

tan(π/20) tan(3π/20) tan(5π/20) tan(7π/20) tan(9π/20)

= tan(π/20) tan(3π/20) tan(5π/20) cot(π/2 - 7π/20) cot(π/2 - 9π/20)

via cofunction identity

= tan(π/20) tan(3π/20) tan(5π/20) cot(3π/20) cot(π/20)

= tan(π/20) tan(3π/20) tan(5π/20) * 1/tan(3π/20) * 1/tan(π/20)

= tan(5π/20)

= tan(π/4)

= 1.

hope it is helpful :)