Question

Prove
cot 2A = cot²A-1/2 cotA​

Answer 1

Step-by-step explanation:

2cot 2A= 2cos2A/sin2A

Double angle identities for :-

Cos2A = Cos²Α−Sin²Α

Sin2A= 2SinACosA

Put the value of Cos2A and Sin2A

2cot2A = 2(cos²Α-sin²Α)/2sinA cosA

2cot2A = (cos²Α/sinAcosA)-(sin²A/sinAcosA

2cot2A= cotA - tanA

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Answer 2

Step-by-step explanation:

$tan 2A = 2tanA / (1 - tan^{2}A)$

$cot 2A = 1/tan 2A$

⇒$cot 2A = (1-tan^{2}A) / 2tan A$

⇒$cot2A = (1-1/cot^2A) / (2/cotA)$$cot 2A = [(cot^2A-1)/cot^{2}A]*(cotA/2)$

⇒$cot2A = (cot^{2}A -1)/2cotA$

Hence, proved

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