Answers

2014-08-17T10:36:45+05:30
Formulas used :-
(1). sin(A) cos(B) - cos(A) sin(B) = sin(A - B)
(2). 2 sin(A) cos(A) = sin(2A)

Proof :-

\frac{1}{sin(10)} -  \frac{ \sqrt{3} }{cos(10)} \\  \\  4 [ \frac{ \frac{1}{2} cos(10) -  \frac{ \sqrt{3} }{2} sin(10) }{2 sin(10) cos(10)} ]  \\  \\   4[ \frac{sin(30) cos(10) - cos(30) sin(10)}{2 sin(10) cos(10)} ] \\  \\ 4[ \frac{sin(20)}{sin(20)} ] \\  \\ 4
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2014-08-17T14:53:43+05:30

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1/sin10-√3/cos10
= (cos10 - 
√3sin10)/cos10sin10
multiplying 1/2 in denominator and numerator
= {(cos10/2) - (√3sin10/2)}/(cos10sin10/2)
= (cos60cos10 - sin60sin10)/(cos10sin10/2)
= cos(60 + 10)/(cos10sin10/2)
= cos70/(cos10sin10/2)
= 2cos70/cos10sin10
multiplying 2 on numerator and denominator
= 4cos70/2sin10cos10
=4cos70/sin20
=4cos70/cos70
= 4  proved

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