Question

in a cyclic quadrilateral then prove that tan A/2 × tan C/2 =1​

Answer 1

Step-by-step explanation:

Given that : ABCD is a cyclic quadrilateral.

According to Cyclic Quadrilateral property, 'Sum of the opposite angles of a cyclic quadrilateral is 180

∘

'.

That is, ∠A+∠C=180

∘

∴ ∠A=180

∘

−∠C ....(i)

According to question we need to find the value of (tanA+tanC)

tanA+tanC

=tan(180−C)+tanC ...From eq.(i)

[Since we know that, tan(180

∘

−θ)=−tanθ

So, tan(180−C)=−tanC]

∴ tan(180−C)+tanC

=−tanC+tanC

=0

Hence, option A is correct.