Question

show that tan7°.tan23°.tan67°.tan83°=1​

Answer 1

HELLO FRIENDS ,

tan(90*-83*) . tan(90* - 67 *) . tan 67* . tan 83 *

as ,{ tan (90*- A) = cot A }

SO, therefore , cot 83* . cot 67* .tan 67* . tan 83*

and now we know that ,( tanA . cot A =1 )

THEREFORE ,

cot 83* . tan 83* . cot 67* . tan 67* =1  hence proved

Answer 2

tan7.cot(90-23).tan(67).cot(90-7)

tan7.cot67.tan67.cot7

1