(sec A+tan A)(1-sin A)=..........

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8. Introduction to Trigonometry

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$(\sec A+\tan A)(1-\sin A)=..........$

A

$\sec A$

B

$\sin A$

C

$\cos A$

D

$\operatorname{cosec} A$

Solution

$(\sec A+\tan A)(1-\sin A)$

$=\left(\frac{1}{\cos A}+\frac{\sin A}{\cos A}\right)(1-\sin A)$

$=\left(\frac{1+\sin A}{\cos A}\right)(1-\sin A)$

$=\frac{1-\sin ^{2} A}{\cos A}=\frac{\cos ^{2} A}{\cos A}$

$=\cos A$

Standard 10

Mathematics

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