Math, asked by abhi31104, 1 year ago

tan A - cotA = 1-2 cos2A
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sin A cos A

Answers

Answered by abdul9838
7

 <b> <body \: bgcolor = "skyblue">

 \huge \bf \: hola \\  \\  \bf \: hey \: dude \: here \: is \: ur \: ans \\  \\  \\   \bf \:  \frac{tan \: a - cot \: a}{sin \: a \times cos \: a  }  = 1 - 2cos^{2} a \\  \\  \bf \: taking \: lhs \\  \\  \bf \:  \frac{tan \: a - cot \: a}{sin \: a \times cos \: a}  \\  \\  \bf \: as \: we \: can \: write \\  \\  \bf \:  \frac{ \frac{sin \: a}{cos \: a} -  \frac{cos \: a}{sin \: a}  }{sin \: a \times cos \: a}  \\  \\  \bf \:  \frac{ \frac{ {sin}^{2}a -  {cos}^{2} a }{  sin \: a \times cos \: a} }{sin \: a \times cos \: a} \\  \\  \bf \:  \frac{ {sin}^{2}a -  {cos}^{2} a }{ \cancel{sin \: a \times cos \: a}}   \times  \frac{ \cancel {\: sin \: a \times cos }\: a}{1}   \\  \\  \bf \:  {sin}^{2} a -  {cos}^{2} a \\  \\  \bf \: as \: we \: know \: that \\  \\  \bf \:  {sin}^{2} a +  {cos}^{2} a = 1 \\  \\  \bf \therefore \:  {sin}^{2} a = 1 -  {cos}^{2} a \\  \\  \bf \huge \: now \\  \\  \bf \: 1 -  {cos}^{2} a -  {cos}^{2} a \\  \\ \bf \:  1 - 2 {cos}^{2} a \\  \\  \bf \therefore \: lhs = rhs \:  \:  \: proved


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