Question

Prove:
(1/tanA)-(1/tan2A)=1/sin2A

Answer 1

• Step-by-step explanation:

Prove that: 1tanA−1tan2A=1sin2A

Solution:

= 1tanA−1tan2A

= 1sinAcosA−1sin2Acos2A

= cosAsinA−cos2Asin2A

= cosA⋅sin2A−cos2A⋅sinAsinA⋅sin2A

= sin2A⋅cosA−cos2A⋅sinAsinA⋅sin2A

= sin(2A−A)sinA⋅sin2A

= sinAsinA⋅sin2A

= 1sin2A

= RHS

Explanation to the above answer.

Step 1: Copying the L.H.S. from the question.

Step 2: Expressing tan in terms of sin and cos because we need sin in the RHS. (tan = sin/cos)

Step 3: We had a/b ÷ c/d in the expression which we can write as ad/bc.

Step 4: Take the LHS and perform the mathematics accordingly.

Step 5: Rearrange the expression to match it in the form of sinAcosB -cosAsinB.

Step 6: In the numerator, we get the expanded formula of sin(A-B) which we can write as sin(A-B).

Step 7: (2A-A) = A. So, we re-write the expression after solving sin(2A-A).

Step 8: The sinA in the numerator as well as in the denominator gets divided and result 1. And, we write the remaining expression as our answer.