Answers

2015-12-17T02:02:41+05:30
√(a-b)/a+b)+ √(a+b)/(a-b)
=√(a-b)²+(a+b)²/√(a²-b²)
=(a+b-2√ab+a+b+2√ab) /√(a²-b²)
=2(a+b)/√(a²-b²)
On squaring,we get
4(a+b)(a+b)/(a+b)(a-b)
=4(a+b)/(a-b)
=(4a/a-b)+(4b/a-b)
put b=a.sin0 note:0=theta
=4a(1+sin0)/a(1-sin0)
=(4+4sin0)/(1-sin0)
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2015-12-18T18:50:31+05:30
Sin x = b/a . I am gonna tell you a beautiful transformation of such fractions .

Let us consider only ( a - b ) / ( a + b ) . Now divide both the numerator and denominator by a .

1/a ( a-b ) / 1/a ( a + b ) = ( 1 - b/a ) / ( 1 + b/a )

Saw how simple that was !

Similarily ( a + b ) / ( a - b ) = ( 1 + b/a ) / ( 1 - b/a )

So our required expression would be

sqrt ( 1 - b/a ) / ( 1 + b/a ) + sqrt ( 1 + b/a ) / ( 1 - b/a )

Replace with b/a with sin x

sqrt ( 1 - sin x ) / ( 1 + sin x ) + sqrt ( 1 + sinx ) / ( 1 - sin x )

Do fraction addition

= ( 1 - sin x ) + ( 1 + sin x ) / sqrt ( 1 - sin^2 x )

= 2 / sqrt ( cos^2 x ) = 2/|cos x| = 2|sec x |

Note* : Some books tend to ignore | | .
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