Question

if tanΦ+secΦ=8,the secΦ-tan it is​

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

Answer 2

$\underline{\red{Answer:}}$

$\boxed{\sf{Property:}}$

$\sf{If \ sec\theta+ tan\theta=m, \ then} \\ \\ \sf{sec\theta - tan\theta=\dfrac{1}{m}} \\ \\ \sf{\therefore{sec\theta-tan\theta =\dfrac{1}{8}}}$