Question

please prove it please ​

Answer 1

Solution:-

=) √{(1+cosA)/(1-cosA)}

Multiplying by √(1 + cosA) on both Numerator and Denominator.

=) √{(1+cosA)/(1-cosA)} × √{(1+cosA)/(1+cosA)}

=) √{ (1+cosA)²/ (1² - cos²A)

=) √{ (1 + cosA)² / sin²A

=) (1+ cosA)/sinA

Hence Proved!

Identity Used:-

( 1² - cos²A) = sin²A

Answer 2

Answer:-

$\frac{ \sqrt{1 + \cos(x) } }{ \sqrt{1 - \cos(x) } }$

Multiplying by √( 1 + cos x) in Numerator and Denominator.

$\frac{ \sqrt{1 + \cos(x) } }{ \sqrt{1 - \cos(x) } } \times \frac{ \sqrt{1 + \cos(x) } }{ \sqrt{1 + \cos(x) } } \\ \\ \frac{ {(1 + \cos(x) })^{2} }{ {1}^{2} - {( \cos(x)) }^{2} }$

$\frac{ \sqrt{ {(1 + \cos(x) )}^{2} } }{ \sqrt{ { \sin(x) }^{2} } } \\ \\ \frac{1 + \cos(x) }{ \sin(x) }$

Hence Proved!

Identity Used.

• ( a + b) × ( a + b) = ( a + b)²

• ( a + b) × ( a - b) = a² - b²