Question

prove that cotA-tanA=2cotA

Answer 1

solution

:-

LHS = cot A - tan A

= cotA - 1/cotA

= (cot²A - 1)/cotA ………………. LHS

RHS = 2 cot2A

=2 *(1-tan²A) / 2tanA

= 2 *{ 1 - (1/cot² A) } /2tanA

= 2 *{(cot²A - 1) / cot²A} / {(2/cotA)}

= 2 * {(cot²A -1) / (2cotA) }

= ( cot²A -1 ) / cotA ……………. RHS

=> LHS = RHS

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Answer 2

Answer:

Step-by-step explanation:

cotA-tanA

=cosA/sinA-sina/cosA

=(cos²A-sin²A)/sinA.cosA

=(cos2A)/(1/2.sin2A)

=2.(cos2A/sin2A)

=2.cot2A , Proved.