Question

simplify sec(1-sina)(seca+tana)​

Answer 1

Answer:

1

Step-by-step explanation

I suppose, the question is

sec a(1- sin a)(sec a + tan a)

=1/cos a(1-sin a)   *        (sec a + tan a)                        {sec a=1/cos a}

=((1/cos a)-(sin a/cos a))(sec a +tan a)

=(sec a     -   tan a        )(sec a +tan a)

Applying (A-B)(A+B)=$A^{2} - B^{2}$

where A=sec a; B=tan a

The equation becomes,

$A^{2} - B^{2}$

= $sec a^{2} - tan a^{2}$

Using properties of trigonometric functions, we know that,

$sec a^{2} - tan a^{2}$=1

Therefore, the final answer is 1