Question

(1-sina)(1+sina)/cosa,

Answer 1

Ответ:

$\frac{(1 - \sin( \alpha ))(1 + \sin( \alpha )) }{ \cos( \alpha ) } = \frac{1 - \sin {}^{2} ( \alpha ) }{ \cos( \alpha ) } = \\ = \frac{ \cos {}^{2} ( \alpha ) }{ \cos( \alpha ) } = \cos( \alpha )$

Answer 2

To simplify the expression (1 - sin(a))(1 + sin(a))/cos(a), you can use trigonometric identities. Start by expanding the numerator and then simplifying it:

(1 - sin(a))(1 + sin(a)) = 1 - sin^2(a)

Now, you can use the Pythagorean identity sin^2(a) + cos^2(a) = 1 to simplify sin^2(a):

1 - sin^2(a) = cos^2(a)

So, the expression becomes:

cos^2(a)/cos(a)

Now, you can cancel one factor of cos(a) from the numerator and denominator:

cos(a)

So, the simplified expression is just cos(a).