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  • 1 answers

Santosh Deshmukh 8 years, 2 months ago

{tex}\begin{array}{l}\int\frac1{\sin x\;+\;\cos x}dx\\putting\rightarrow\;\;\sin x\;=\;\frac{2\tan{\displaystyle\frac x2}}{1+\tan^2{\displaystyle\frac x2}}\;\;and\;\cos x\;=\;\frac{1-\tan^2{\displaystyle\frac x2}}{1+t\mathrm{an}^2\frac x2}\;\\we\;get\;\int\frac{1+\tan^2\frac x2}{1+2\tan{\displaystyle\frac x2}-\tan^2{\displaystyle\frac x2}}dx\;=\;\int\frac{\displaystyle sec^2\frac x2}{\displaystyle1+2\tan\frac x2-\tan^2\frac x2}dx\\let\;\tan\frac x2\;=\;t\;\Rightarrow\;sec^2\frac x2dx\;=\;2dt\\\Rightarrow\;\int\frac{2dt}{1\;+\;2t\;\;-\;t^2}\;\;=\;\int\frac{2dt}{{\displaystyle\left(\sqrt2\right)^2}{\displaystyle-}{\displaystyle{\displaystyle\left(t-1\right)}^2}}\\=\;2\;\log\left|\frac{\displaystyle\sqrt2+t-1}{{\displaystyle\sqrt2}{\displaystyle-}t+1}\right|\;+\;c\;=\;2\;\log\;\left|\frac{\sqrt2{\displaystyle-}{\displaystyle1}{\displaystyle+}{\displaystyle\;}{\displaystyle\tan}{\displaystyle\frac x2}}{\sqrt2{\displaystyle+}1-\;\tan\frac x2}\right|\;+\;c\\\\\end{array}{/tex}

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Bhat Rayees 8 years, 2 months ago

0÷0=10 Multiply b/s by 0 0= 10×0 0=0 lhs=rhs
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Harsh Singh 8 years, 2 months ago

Bro there is no easy way in maths but there is a trick try the elementary operation in your board paper solution as given in your NCERT book using 'A=IA' and built it into last extent if you think that you are wrong at the last stage of elementary operation use the methods of determenent i.e; A inverse is equal to adj(A) Divided by determinent of A and you will get full mark for this question
1+2
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Roshan Raj 8 years, 2 months ago

.6990

Sanya Chauhan 8 years, 2 months ago

1/5
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Himanshu Kumar 8 years, 2 months ago

NOTE = question is incomplete OK First of all check it is continuous and defferentiable and then check f(a)=f (b) And then verify it , F'(x)=0
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Ankit Singh 8 years, 2 months ago

Take x-y=t then derivate it with respect to t
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Viksit Singh Padam 8 years, 2 months ago

Integral xcos(πx) By using product rule it will be X[sin(πx)] ÷π -integral sin(πx) X[sin(πx)] ÷π -[-cos(πx) ÷π] Xsin(πx) ÷π+cos(πx) Its ans. Tnx u
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Sumiti Beniwal 8 years, 2 months ago

Arihant

Rohit Singh 8 years, 2 months ago

Oswal
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Arti Kumari 8 years, 2 months ago

Directly by using discriminant method
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Richa Hajowary 8 years, 2 months ago

-sin x
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