Question

Cosec2a+cosec4a=cota-cot4a​

Answer 1

Answer: Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A

Explanation:

Taking LHS :

⇒Cosec 2 A + Cot 4 A

⇒Cosec 2 A + ( Cot 2 A )2

⇒Cosec 2 A + ( Cosec 2 A - 1 )2 ( we know : 1 + Cot 2 θ = Cosec 2 θ )

⇒Cosec 2 A + Cosec 4 A + 1 - 2 Cosec 2 A

⇒ Cosec 4 A + 1 - Cosec 2 A

⇒ Cosec 4 A + 1 - ( 1 + Cot 2 A)

⇒ Cosec 4 A + 1 - 1 - Cot 2 A

⇒ Cosec 4 A - Cot 2 A

or cosec2A+cosec4A=cotA-cot4A