(1+tan
A) cot A/cosec2 A
= tan A
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Given : (1+tan ²A) cot A/cosec²A = tan A
To find : Prove that (1+tan ²A) cot A/cosec²A = tan A
Solution:
Correct Question is
(1+tan ²A) cot A/cosec²A = tan A
LHS = (1+tan A) cot A/cosec²A
using cot A = CosA/SinA
& 1/cosec²A = Sin²A
= (1+tan ²A) (CosA/SinA) Sin²A
= (1+tan ²A) (CosASinA )
= (1 + Sin²A/Cos²A) (CosASinA)
= (Cos²A + Sin²A) (CosASinA) / Cos²A
= (1) SinA/CosA
= TanA
= RHS
(1+tan ²A) cot A/cosec²A = tan A
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