1-tan 2 A 1-1 - tan 2 A -1 - sin 2 A -sin 4 A

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Implicit Differentiation

1+tan 2 A 1+1...

Question

(1+tan²A) (1+1/tan²A) = 1/sin²A-sin⁴A

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(1 + {tan}^{2} A) (1 + \frac{1}{{tan}^{2} A}) = \frac{1}{{sin}^{2} A - {sin}^{4} A}

Prove the following trigonometric identities:

$(1 + t a n^{2} A) + (1 + \frac{1}{t a n^{2} A}) = \frac{1}{s i n^{2} A - s i n^{4} A}$

(1 + \frac{1}{{tan}^{2} A}) \times (1 + \frac{1}{{cot}^{2} A}) = \frac{1}{{sin}^{2} A - {sin}^{4} A}

\frac{1 - \tan^{2} A}{1 + \tan^{2} A} = \cos^{2} A - \sin^{2} A

\sin 2 A = \frac{2 \tan A}{1 + \tan^{2} A}

\cos 2 A = \frac{1 - \tan^{2} A}{1 + \tan^{2} A}

\tan 2 A = \frac{2 \tan A}{1 - \tan^{2} A}

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