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Solve the following equation for xcos(tan-1 x)=sin(cot-14)3 |
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Answer» Cos(tan⁻¹x)=sin(cot⁻¹3/4)Let, cot⁻¹(3/4)=yor, coty=3/4(=perpendicular/base)Using Pythagorus's theorem,hypotenuse=√(p²+b²)=√(3²+4²)=√25=5∴, siny(=p/h)=3/5∴, sin(cot⁻¹3/4)=siny=3/5cos(tan⁻¹x)=3/5or, tan⁻¹x=cos⁻¹(3/5)Again let, cos⁻¹(3/5)=zor, cosz=3/5=base/hypotenuse∴, perpendicular=√5²-3²=√16=4∴, tanz=p/b=4/3∴, tan⁻¹x=zor, x=tanzor, x=4/3 |
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