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:
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