Question

tan 10° tan 15° tan 75° tan 80° = 1

Answer 1

tan 10 tan 80 tan15 tan 75 = 1
tan (90-80).tan 80 tan15 tan (90-15) = 1

tan (90- @) = Cot @

Cot 80.Tan 80 tan 15.Cot 15= 1

we know that 1/cot = tan

1/tan80×tan 80 1/ cot 15× cot 15 = 1
1= 1

Answer 2

Hey

To prove :-

tan 10° tan 15° tan 75° tan 80° = 1

= tan 10° tan 15° tan ( 90° - 15°) tan(90° - 10° )

= tan 10° tan 15° cot 15° cot 10°

= tan 10° * 1 / tan 10° * tan 15° * 1 / tan 15°

= 1 * 1

= 1

thanks :)