cosA/(cosA -sinA) - cosA/(cosA +sinA) = tan2A | Prove the trigonometric identity | SciPiPupil

Question: Prove the following trigonometric identity: $\dfrac{cosA}{cosA -sinA} - \dfrac{cosA}{cosA +sinA}$ = tan2A

Solution:

LHS

= $\dfrac{cosA}{cosA -sinA} - \dfrac{cosA}{cosA +sinA}$

= $\dfrac{cosA(cosA +sinA) -cosA(cosA -sinA}{(cosA -sinA)(cosA +sinA)}$

= $\dfrac{cosA (cosA +sinA -cosA +sinA}{cos²A -sin²A}$

= $\dfrac{cosA(2sinA)}{cos 2A}$

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

= $\dfrac{sin 2A}{cos 2A}$

= $tan 2A$

RHS

Related Notes And Solutions:

Link: Introduction To Trigonometry

Link: Values of Trigonometric Ratios

Link: Compound Angles

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