Prove the following trigonometric identities-cos-cos-tan 2-sin 2-

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Complementary Trigonometric Ratios

Prove the fol...

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Prove the following trigonometric identities.

(secθ + cosθ) (secθ − cosθ) = tan²θ + sin²θ

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(sec θ + cos θ) (sec θ - cos θ) = {tan}^{2} θ + {sin}^{2} θ

Prove the following trigonometric identities:

$\frac{1 + s e c θ}{s e c θ} = \frac{s i n^{2} θ}{1 - c o s θ}$

\frac{\tan^{2} θ}{(1 + \tan^{2} θ)} = \sin^{2} θ

\frac{cotθ + cosθ}{cotθ - cosθ} = \frac{1 + sinθ}{1 - sinθ}

Prove the following trigonometric identities:

$\frac{(1 + s i n θ)^{2} + (1 - s i n θ)^{2}}{2 c o s^{2} θ} = \frac{1 + s i n^{2} θ}{1 - s i n^{2} θ}$

\frac{{tan}^{2} θ}{{tan}^{2} θ - 1} + \frac{c o s e c^{2} θ}{{sec}^{2} θ - c o s e c^{2} θ} = \frac{1}{{sin}^{2} θ - {cos}^{2} θ}

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