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dx/(sinx-cosx)

dx/(sinx-cosx)

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1 Answers

bhushan thakur
14 Points
10 years ago

write cosx as sin(pi/2 -x).then use sinC - sinD formula.that is sinx - sin(pi/2 -x)=2cos(pi/4)sin(x-pi/4)=root2*sin(x-pi/4)

replace sinx -cosx by above value and integrate.

∫dx/root2*sin(x-pi/4)=1/root2∫cosec(x-pi/4)dx=1/root2 log[cosec(x-pi/4) - cot(x-pi/4)]

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