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Find the value of sin A

Posted March 24th, 2008 by alpha
in

Given A is less than 90 degree
tanA +secA=2
then sinA has value-

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Answer

On March 24th, 2008 Structure says:

$ \tan a+\sec a=2 $

$$\tan a+\sec a=\frac{\sin a+1}{\cos a}=\frac{(\cos \frac{a}{2}+\sin \frac{a}{2})^2}{\cos^2 \frac{a}{2}-\sin ^2\frac{a}{2}}=\frac{\cos \frac{a}{2}+\sin \frac{a}{2}}{\cos \frac{a}{2}-\sin \frac{a}{2}}=\frac{1+\tan \frac{a}{2}}{1-\tan \frac{a}{2}}=2$$
$$\tan \frac{a}{2}=\frac{1}{3}$$
$$\sin a=\frac{2\tan \frac{a}{2}}{1+\tan^2 \frac{a}{2}}=\frac{2\frac{1}{3}}{1+\frac{1}{9}}=\frac{3}{5}$$

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