Choose the correct option. Justify your choice. 1 + tan2A/1 + cot2A =? (A) sec2 A (B) -1 (C) cot2A (D) tan2A

Answer: (D) tan2A

We know that,

tan2A =1/cot2A

Now, substitute this in the given equation, we get

1 + tan2A/1 + cot2A

= (1 + 1/cot2A)/1 + cot2A

= (cot2A + 1/cot2A) ×(1/1 + cot2A)

= 1/cot2A

= tan2A

So, 1+tan2A/1+cot2A = tan2A

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