sin 8A/sin 4A - cos 8A/cos 4A = sec 4A | Prove the trigonometric identity | SciPiPupil

Question: Prove the following trigonometric identity: $\dfrac{sin 8A}{sin 4A} - \dfrac{cos 8A}{cos 4A}$ = sec 4A.

Solution:

LHS

= $\dfrac{sin 8A}{sin 4A} - \dfrac{cos 8A}{cos 4A}$

= $\dfrac{sin 8A.cos4A - cos8A.sin4A}{sin 4A.cos 4A}$

= $\dfrac{sin (8A -4A)}{sin 4A.cos4A}$

= $\dfrac{sin 4A}{sin4A.cos4A}$

= $\dfrac{1}{cos 4A}$

= $sec 4A$

= RHS

Related Notes And Solutions:

Link: Introduction To Trigonometry

Link: Values of Trigonometric Ratios

Link: Compound Angles

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