Answers

2014-08-21T16:26:07+05:30
This is not 5 points question, because this is easy but yeah not that easy,

first of all lets do few things in advance
(1)
\frac{1}{sin^{2}x} +  \frac{1}{cos^{2}x} \\\\= \frac{sin^{2}x+cos^{2}x}{sin^{2}xcos^{2}x}  \\ \\ =  \frac{1}{sin^{2}xcos^{2}x}


(2)
\frac{sinx}{cosx} +  \frac{cosx}{sinx} \\  \\ = \frac{sin^{2}x + cos^{2}x}{sinxcosx} \\  \\  \frac{1}{sinxcosx}

Proof;
(sinA +  \frac{1}{cosA})^{2} + (cosA +  \frac{1}{sinA})^{2} \\  \\  sin^{2}A +  \frac{1}{cos^{2}A} + 2 \frac{sinA}{cosA} + cos^{2}A + \frac{1}{sin^{2}A} + 2 \frac{cosA}{sinA} \\  \\ [sin^{2}A + cos^{2}A] + [\frac{1}{sin^{2}A} + \frac{1}{cos^{2}A}] + 2[\frac{sinA}{cosA} + \frac{cosA}{sinA}] \\  \\ 1 + \frac{1}{sin^{2}Acos^{2}A} + \frac{2}{sinAcosA} \\  \\  (1 + \frac{1}{sinAcosA})^{2} \\  \\ (1 + secAcosecA)^{2}
1 2 1