Question
Prove that:
$\Big(\frac{\sin49^\circ}{\cos41^\circ}\Big)^2+\Big(\frac{\cos41^\circ}{\sin49^\circ}\Big)^2=2$
$\Big(\frac{\sin49^\circ}{\cos41^\circ}\Big)^2+\Big(\frac{\cos41^\circ}{\sin49^\circ}\Big)^2=2$
✓
Answer
$\text{L.H.S.}=\Big(\frac{\sin49^\circ}{\cos41^\circ}\Big)^2+\Big(\frac{\cos41^\circ}{\sin49^\circ}\Big)^2$
$=\Big(\frac{\cos(90^\circ-49^\circ)}{\cos41^\circ}\Big)^2+\Big(\frac{\cos41^\circ}{\cos(90^\circ-49^\circ)}\Big)^2$
$=\Big(\frac{\cos41^\circ}{\cos41^\circ}\Big)^2+\Big(\frac{\cos41^\circ}{\cos41^\circ}\Big)^2$
$=1^2+1^2$
$=1+1$
$=2$
$=\text{R.H.S.}$
Disclaimer: The RHS of (v) given in textbook is incorrect. There should be 2 instead 1. The same has been corrected in the solution here.
$=\Big(\frac{\cos(90^\circ-49^\circ)}{\cos41^\circ}\Big)^2+\Big(\frac{\cos41^\circ}{\cos(90^\circ-49^\circ)}\Big)^2$
$=\Big(\frac{\cos41^\circ}{\cos41^\circ}\Big)^2+\Big(\frac{\cos41^\circ}{\cos41^\circ}\Big)^2$
$=1^2+1^2$
$=1+1$
$=2$
$=\text{R.H.S.}$
Disclaimer: The RHS of (v) given in textbook is incorrect. There should be 2 instead 1. The same has been corrected in the solution here.
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