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2015-04-02T16:33:12+05:30

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 3) Cos . 1/ sin= cot
        cot=cot
          hence proved
1 5 1
Cool!!!!!!!!!
yeah!now u solve
for the 1st 1 try using complementary angles
s correct
did u get???
The Brainliest Answer!
2015-04-02T19:19:03+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Please check if the numbers given in the first problem are correct or not.

\frac{Sin 19 }{Sin 71}-\frac{Cos11}{cos 19}\\\\=\frac{Sin 19 }{Cos(90-71)}-\frac{Cos11}{cos 19}\\\\=\frac{Sin19\ -\ Cos11}{Cos19}\\\\

If there is Sin 79  instead of  Sin 19 in the first ratio, then the answer would be zero.  Because, Sin 79 = Cos (90 - 79) = Cos 11.   Or, perhaps there is Cos 71 instead of Cos 11 in the second ratio.  Then also the answer is 0.

 If there is no mistake in the given problem, then:

\frac{Sin19\ -\ Cos11}{Cos19}\\\\=tan19-\frac{Sin(90-11)}{Cos19}\\\\=tan19-\frac{sin(60+19)}{cos19}\\\\tan19-\frac{sin60\ cos19+cos60\ sin19}{cos19}\\\\=tan19-\frac{\sqrt3}{2}-\frac{1}{2}tan19\\\\=-\frac{\sqrt3-tan19}{2}
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One must use parentheses () [] {}  to clearly write the expressions,  Otherwise, we have confusion in understanding.

\frac{\sqrt3\ cos23-sin23}{2}=\frac{\sqrt3}{2} cos23}-\frac{1}{2}Sin23\\\\=Cos30\ Cos23-Sin30 \ Sin23\\\\Cos(30+23)=Cos53\\
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         CosФ * Cosec Ф
         Cos Ф * 1/ Sin Ф
        = Cos Ф / Sin Ф  = Cot Ф

2 5 2
how did u get the 1st answer sir?
pls sir faast
i showed the method above.. we use the formula: Cos A = Sin (90-A) and Sin A = Cos (90- A).
i did not understand the 7th and 8th step.
expansion of Sin (A + B)