Question

Find the set of values of a-"R" , such that
tan^2 x + sec^2 x = a holds for some a

Answer 1

I have solved the question , and i am left with three conditions

Answer 2

\[\huge a \ge 1 \]
or
\[\huge a \ge -1\]

and
\[\huge a \ge \frac{ -5 }{ 4 }\]

I am stuck here , wether i should take union or intersection

Answer 3

(not verifying whether those conditions are correct)*

be careful with the usage of "and"s and "or"s

its (1st condition) OR (2nd condition) OR (3rd condition)
right ??
because 'a' cannot take 2 values at a time,
for example, saying a=10 AND a=11 for one equation is incorrect

Answer 4

yup , i carefuly used that

Answer 5

OR \(\equiv\) Union

Answer 6

and is intersection?

Answer 7

so union of 1st and 2nd , let say it is y
thus
y intersection the third condition

Answer 8

?

Answer 9

yes, AND = Intersection

if your "and" is correct, then yes
what u said is correct

Answer 10

yes getting a correct answer and is given the textbook
-1 to infinity
thank you again ^_^

Answer 11

welcome ^_^