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✌1+(cot2A-tan2A)cos2A=cot2A​✌.
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Answer 1

Answer:

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Answer 2

Given :    1  + ( Cot²A  - Tan²A)Cos²A  = Cot²A

To find : Prove that 1  + ( Cot²A  - Tan²A)Cos²A  = Cot²A

Solution:

1  + ( Cot²A  - Tan²A)Cos²A  = Cot²A

LHS =

1  + ( Cot²A  - Tan²A)Cos²A

using Cot = Cos/Sin  & Tan = Sin/Cos

= 1  + ( Cos²A/Sin²A  -Sin²A/Cos²A )Cos²A

= 1  + (( Cos⁴A - Sin⁴A) /Sin²ACos²A)Cos²A

=  1  +  ( Cos⁴A - Sin⁴A) /Sin²A

using a² - b² = ( a + b)(a - b)

here a = Cos²A  & b = Sin²A

= 1  + (Cos²A + Sin²A)(Cos²A - Sin²A)/Sin²A

using Cos²A + Sin²A = 1

= 1  +  (Cos²A - Sin²A)/Sin²A

= (Sin²A + Cos²A - Sin²A)/Sin²A

= Cos²A/Sin²A

= Cot²A  

= RHS

QED

Hence Proved

1  + ( Cot²A  - Tan²A)Cos²A  = Cot²A

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