Some Applications of Trigonometry

Express the ratios cos A, tan A, cot A and sec A in terms of sin A. - Wired Faculty

Question

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

Solution

$because space space sin squared straight A space plus space cos squared straight A space equals space 1 rightwards double arrow space space space space space space space space cos squared straight A space equals space 1 minus sin squared straight A rightwards double arrow space space space space space space space space cosA space equals space plus-or-minus square root of 1 minus sin squared straight A end root$
This gives, $cos space straight A space equals space square root of 1 minus sin squared straight A end root$
Hence,
$tanA space equals space sinA over cosA equals fraction numerator sinA over denominator square root of 1 minus sin squared straight A end root end fraction cotA space equals space cosA over sinA space equals space fraction numerator square root of 1 minus sin squared straight A end root over denominator sinA end fraction$
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Some Applications Of Trigonometry

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

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