SSC CGL 8 Aug 2017 Shift 1 Paper

Question : 71 of 100

Marks: +1, -0

What is the simplified value of

1 + \tan A\tan (A/2)?

Solution:

1+\tanA \tan A/2

=1+\sinA/\cosA×{ \sin A/2}/{\cos A/2}

{{\cos A.{\cos A/2}+{\sin A}.{\sin A/2}}/{{\cos A}.{\cos A/2}}

{ (1-2\sin^2A/2)\cos A/2}

{1+2{\sin A/2}{\cos A/2}{\sin A/2}}/{{\cos A}.{\cos A/2}}

{{\cos A/2}-2\sin^2A/2\cos A/2}

{1-2\sin^2A/2\cos A/2}/{{\cos A}.{\cos A/2}}

{\cos A/2}/{{\cos A}.{\cos A/2}}=1/\cosA=\secA

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