Prove the following trigonometric identities- 1-tan2A-1-1-tan2A -1-sin2A-sin4A

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Trigonometric Identities

Prove the fol...

Question

Prove the following trigonometric identities:

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

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

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

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

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

(1+tan²A) (1+1/tan²A) = 1/sin²A-sin⁴A

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