Math, asked by rithviknani9221, 9 months ago

Tan2a+cot2a=sec2acosec2a-2

Answers

Answered by llxdevilgirlxll

9

$<h1 data-shadow='Answer!'>Answer!</h1>$

${ \ LHS \ = \ tan ² A \ + \ cot ² A}$

⇢ $\frac{sin²A}{cos ²A}$ + $\frac{cos² A}{sin²A}$

⇢ $\frac{sin⁴A + cos⁴A}{sin ²A cos²A}$

⇢ $\frac{1-2sin²A cos²A}{sin²A cos²A}$

⇢ $\frac{1-2sin²A cos²A}{sin ²A cos²A}$

⇢ $\frac{1}{cos²A}$ × $\frac{1}{sin²A}$ ${ \ - 2}$

⇢ ${ \sec²A \ × \ cosec²A \ - 2}$

⇢ ${ \ RHS}$

⇢ ${ \ Hence \ proved}$

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