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2014-08-03T21:41:09+05:30

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 sin^{2} A / cos ^{2} A  +  cos ^{2} A / sin ^{2} A  

(sin ^{4} A + cos ^{4} A ) / sin^{2} A  cos ^{2} A

[  (sin^{2} A + cos^{2} A )^{2}  - 2 cos^{2} A  sin^{2} A   ]  / cos ^{2} A  sin^{2} A

[ 1 - 2 cos^{2} A sin^{2} A ] /  cos^{2} A  sin ^{2} A

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

sec^{2} A cosec^{2} A  - 2


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i used the Pi button in the edit window to write equations. it has generated the script above. I hope it is understood. i hope it is displayed properly o n your screens
The Brainliest Answer!
2014-08-04T02:52:16+05:30
A=x\\\\tan^2x+cot^2x=sec^2xcosec^2x-2\\\\R=\frac{1}{cos^2x}\times\frac{1}{sin^2x}-2=\frac{1}{sin^2xcos^2x}-\frac{2sin^2xcos^2x}{sin^2xcos^2x}\\\\=\frac{1-2sin^2xcos^2x}{sin^2cos^2x}=\frac{sin^2x+cos^2x-sin^2xcos^2x-sin^2xcos^2x}{sin^2xcos^2x}\\\\=\frac{sin^2x-sin^2xcos^2x}{sin^2xcos^2x}+\frac{cos^2x-sin^2xcos^2x}{sin^2xcos^2x}=\frac{sin^2x(1-cos^2x)}{sin^2xcos^2x}+\frac{cos^2x(1-sin^2x)}{sin^2xcos^2x}

=\frac{1-cos^2x}{cos^2x}+\frac{1-sin^2x}{sin^2x}=\frac{sin^2x}{cos^2x}+\frac{cos^2x}{sin^2x}=tan^2x+cot^2x=L


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Used:\\\\sin^2x+cos^2x=1\\\\sin^2x=1-cos^2x\ and\ cos^2x=1-sin^2x\\\\tanx=\frac{sinx}{cosx}\\\\cotx=\frac{cosx}{sinx}\\\\secx=\frac{1}{cosx}\\\\cosecx=\frac{1}{sinx}
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