Prove that: cosec2A +cot2A = cotA | Trigonometric Identities | SciPiPupil

Prove that: $cosec2A +cot2A = cotA$

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.

= $cosec2A +cot2A$

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

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

= $\dfrac{cos2A\;+1}{sin2A}$  

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

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

= $\dfrac{cosA}{sinA}$

= $cotA$

= R.H.S.

Explanation to the above answer.

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

Step 2: In order to carry out further mathematical operations, we write given terms in form of cos2A and sin2A. (cot2A = cos2A/sin2A) and (cosec2A = 1/sin2A)

Step 3: Rewriting the expression by putting second term first. 

Step 4: If the two or more terms have the like denominators, we can always add or subtract those terms. 

Step 5: (cos2A = 2cos²A -1)

Step 6:  (sin2A = 2sinAcosA)

Step 7: Diving the 2cosA in the numerator and denominator gives us cosA/sinA.

Step 8: (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: cosec2A +cot2A = cotA | Trigonometric Identities | SciPiPupil

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