if-tan-2-x-sec-x-a-1-has-at-least-one-solution-then-find-the-complete-set-of-values-of-a-

Question Number 146868 by gsk2684 last updated on 16/Jul/21

i f \tan^{2} x + \sec x = a + 1 h a s a t l e a s t

o n e s o l u t i o n t h e n f i n d t h e c o m p l e t e s e t

o f v a l u e s o f^{'} a^{'} ?

Answered by Olaf_Thorendsen last updated on 16/Jul/21

\tan^{2} x + \sec x = a + 1 (1)

1 + \tan^{2} x + \sec x = a + 2

\sec^{2} x + \sec x - (a + 2) = 0

Δ = 1^{2} - 4 \times 1 (- (a + 2) = 4 a + 9

(1) has at least one solution if Δ ⩾ 0

\Rightarrow a \in [- \frac{9}{4}; + \infty [

Commented by gsk2684 last updated on 16/Jul/21

t h a n k y o u f o r y o u r c o n c e r n s i r .

p l e a s e v e r i f y t h e b o u n d s o f \sec x

i . e . \sec x ⩽ - 1 o r \sec x ⩾ 1

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