Question

simplify (1+cot*2thita) (1-cos thita) (1+cos thita)

Answer 1

★given:-

$\implies \: (1 + \cot {}^{2} \theta)(1 - \cos \theta)(1 + \cos \theta )$

★find:-

• given quantity value

★solution:-

$\implies \: (1 + \cot {}^{2} \theta )(1 - \cos {}^{} \theta )(1 + \cos \theta)$

$\implies \: (1 + \cot {}^{2} \theta )(1 - \cos {}^{2} \theta )$

$\implies \: ( \cosec {}^{2} \theta) ( \sin {}^{2} \theta)$

$\implies \: \frac{1}{ \cancel{ \sin {}^{2} \theta }} \times \cancel{\sin {}^{2} \theta }$

$\implies \boxed{ \red{1}}$

uses formula

$\implies \star \pink{(a + b)(a - b) = a {}^{2} - b {}^{2} } \\ \\ \implies \star \pink{1 + \cot {}^{2} \theta = \cosec {}^{2} \theta } \\ \\ \implies \star \pink{1 - \cos {}^{2} \theta = \sin {}^{2} \theta } \\ \\ \implies \: \star \pink{\cosec \theta = \frac{1}{ \sin \theta } }$

======================================

I hope it helps you