Prove that : \frac{\cos A}{1+ \sin A}+\tan A= \sec A .

ICSE Class X Math 2016 Solved Paper - Question 51

Question : 51 of 57

Marks: +1, -0

Prove that :

\;{\cos A}/{1+ sin \;A}+\tan A=\ sec A

Solution:

\;\text " L.H.S. "\;\;=\;{\cos {\A}}/{1+ sin \; {\A}}+\tan {\A}

\;=\;{\cos {\A}}/{1+ sin \; {\A}}+\;{ sin \; {\A}}/{\cos {\A}}

\;=\;{\cos ^2 {\A}+ sin \; {\A}(1+ sin \; {\A})}/{(1+ sin \; {\A}) \cos {\A}}

\;=\;{\cos ^2 {\A}+ sin \; {\A}+ sin \;^2 {\A}}/{(1+ sin \; {\A})(\cos {\A})}

\;=\;{1+ sin \; {\A}}/{(1+ sin \; {\A}) \cos {\A}}

\;=\;{1}/{\cos {\A}}

\;=\ sec {\A}=\;\text " R.H.S. "\;

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