Question

please answer fast please 3 and 5 by explanation please​

Answer 1

Answer:

hi good afternoon

Step-by-step explanation:

please mark brain list please follow and thanks

Answer 2

Answer:

K=2

Step-by-step explanation:

(3)

The polynomial is

$p(x) = {x}^{2} - kx + 1$

It has a zero as 1, so

$p(1) = 0 \\ {1}^{2} - k \times 1 + 1 = 0 \\ k = 2$

So value of k is 2

(5)

$\sqrt{ \frac{1 + \sin( \alpha ) }{1 - \sin( \alpha ) } }$

By rationalizing the denominator we get,

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

Now using the identity

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

So the expression can be written as

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

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

$= \sec( \alpha ) + \tan( \alpha )$

Hence proved.