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Express the ratios cos A, tan A and sec A in terms of sin A. - Mathematics

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Sum

Express the ratios cos A, tan A and sec A in terms of sin A.

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Solution

Since cos2A + sin2A = 1, therefore,

cos2A = 1 – sin2A, i.e., cos A = ` \pm \sqrt{1-\sin ^{2}A`

This gives

`cos A = \sqrt{1-\sin^{2}A) `

Hence,

`\tan A=\frac{\sin A}{\cos A}=\frac{\sin A}{\sqrt{1-\sin^{2}}A}\text{ and}`

`\sec A=\frac{1}{\cos A}=\frac{1}{\sqrt{1-\sin ^{2}A}}`

Concept: Trigonometric Identities
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