Question

Please solve this question ​

Prove that ( 1+cot^2 Q ) ( 1 - cos Q ) ( 1+ cos Q ) = 1 ​

Answer 1

( 1+cot² Q ) ( 1 - cos Q ) ( 1+ cos Q ) = 1

Answer 2

$L.H.S. = (1+cot2θ)(1−cosθ)(1+cosθ) \\ ⇒ L.H.S. = (1+cot 2θ)(1−cos 2 θ) \\ ⇒ L.H.S. = cosec 2θsin 2 θ</p><p>[∵1+cot 2θ=cosec 2θand1−cos 2</p><p> θ=sin </p><p>2</p><p> ]</p><p></p><p>⇒ L.H.S. = cosec </p><p>2</p><p> θsin </p><p>2</p><p> θ</p><p></p><p>⇒ L.H.S. = </p><p>sin </p><p>2</p><p> θ</p><p>1</p><p></p><p> ×sin </p><p>2</p><p> θ=1=R.H.S.$