Mathematics

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:
sec² A + cosec² A = sec² A cosec² A.

Trigonometric Identities

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Answer

The L.H.S of the equation can be written as,

$\Rightarrow \dfrac{1}{\text{cos}^2 A} + \dfrac{1}{\text{sin}^2 A} \\[1em] \Rightarrow \dfrac{\text{sin}^2 A +\text{cos}^2 A}{\text{cos}^2 A .\text{ sin}^2 A} \\[1em] \Rightarrow \dfrac{1}{\text{cos}^2 A .\text{ sin}^2 A} \\[1em] \Rightarrow \text{sec}^2 A. \text{cosec}^2 A$

Since, L.H.S. = R.H.S hence, proved that sec² A + cosec² A = sec² A cosec² A.

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Mathematics

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:
sec² A + cosec² A = sec² A cosec² A.

Trigonometric Identities

Answer

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Mathematics

Prove the following identities, where the angles involved are acute angles for which the trigonometric ratios are defined:sec2 A + cosec2 A = sec2 A cosec2 A.

Trigonometric Identities

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