Question

plz frnds solve this question

Answer 1

Tan A / (1+Tan²A) + Cot A / (1+Cot²A) = 2(Sin A × Cos A)

Taking LHS

= Tan A / Sec²A + Cot A / Cosec²A

(because 1+Tan²A = Sec²A  ;  1+Cot²A = Cosec²A)

= (Sin A / Cos A) × Cos²A  +  (Cos A / Sin A) × Sin²A

(because Tan A = Sin A / Cos A  and Cot A = Cos A /Sin A)

(also Sec²A = 1/Cos²A   and   Cosec²A = 1/Sin²A)

= Sin A Cos A  + Sin A Cos A

= 2 Sin A Cos A    = RHS 

Hence Proved.
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