Prove that: (1 +sec2A)/(tan2A) = cotA.


Prove that: $\dfrac {1+sec2A}{tan2A} = cotA$

This is a class 10 Question From Multiple Angles chapter of Unit Trigonometry. All the steps for the solutions are mentioned in the description below. If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts. 

Solution:

Taking L.H.S.

= $\dfrac{1+sec2A}{tan2A}$

= $\dfrac{1}{tan2A}\;+\; \dfrac{sec2A}{tan2A}$

= $cot2A\;+\;cosec2A$

= $\dfrac{cos2A}{sin2A}\;+\;\dfrac{1}{sin2A}$

= $\dfrac{cos2A\;+1}{sin2A}$  

= $\dfrac{2cos^2A\;-1\;+1}{sin2A}$

= $\dfrac{2cos^2A}{2sinAcosA}$

= $\dfrac{cosA}{sinA}$

= $cotA$

= R.H.S.


Explanation to the above answer.


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

Step 2: If two or more terms are in the numerator, we can always seperated the terms, each dividing by the denominator.

Step 3: (1/tan2A = cot2A) and (sec2A/tan2A = cosec2A)

Step 4: (cot2A = cos2A/sin2A) and (cosec2A = 1/sin2A)

Step 5: If the two or more terms have the like denominators, we can always add or subtract those terms. 

Step 6: (cos2A = 2cos²A -1)

Step 7: (sin2A = 2sinAcosA)

Step 8: Dividing the 2cosA in the numerator and denominator gives us cosA/sinA.

Step 9: (cosA/sinA = cotA).


Here is the Facebook link to the solution of this question in image. 

Related Notes:

Link: Introduction To Trigonometry
Link: Values of Trigonometric Ratios
Link: Compound Angles

Question: Prove that: (1 +sec2A)/(tan2A) = cotA. | Trigonometric Identities | SciPiPupil

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