the-equation-of-a-sin-x-a-cos-x-a-has-solution-in-R-hence-a-

Question Number 155878 by mnjuly1970 last updated on 05/Oct/21

t h e e q u a t i o n o f :

(a + s i n (x)) (a + c o s (x)) = a

h a s s o l u t i o n i n R

h e n c e :

a \in ?

Answered by MJS_new last updated on 05/Oct/21

solve it for a and then find the range :

1 - \sqrt{2} ⩽ a ⩽ \frac{1 + \sqrt{2} + \sqrt{1 + 2 \sqrt{2}}}{2}

Commented by talminator2856791 last updated on 05/Oct/21

did you also use wolframalpha ?

Commented by MJS_new last updated on 05/Oct/21

no . I used my own brain .

Answered by talminator2856791 last updated on 05/Oct/21

a \in (1 - \sqrt{2}, \frac{1}{2} + \frac{1}{\sqrt{2}} - \frac{1}{2} \sqrt{1 + 2 \sqrt{2}})