if tan^2 x+sec x=a+1 has at least one solution then find the complete set of values of ′a′?


Question and Answers Forum

All Questions Topic List
Trigonometry Questions
Previous in All Question Next in All Question
Previous in Trigonometry Next in Trigonometry
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

	$t h a n k y o u f o r y o u r c o n c e r n s i r .$ $p l e a s e v e r i f y t h e b o u n d s o f \sec x$ $i . e . \sec x ⩽ - 1 o r \sec x ⩾ 1$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum