Question

prove that
tan 43° . tan 23°. tan42° . tan 67° =1​

Answer 1

Step-by-step explanation:

Before answering your question, let us see two things :

i) We know that tan ∅ = cot (90°-∅)

and

ii) There is a mistake in your question . The correct version would be tan 48° . tan 23°. tan42° . tan 67° =1​

Now coming to the proof,

L.H.S.

= tan 48° * tan 23° * tan (90° - 48°) * tan (90° - 23°)

= tan 48° * tan 23° *cot 48° * cot 23°

= tan 48° *cot 48° * tan 23° * cot 23°

= 1*1

= 1