nice-calculus-if-pq-sin-2-x-pq-cos-2-x-p-q-then-tan-x-

Question Number 139521 by mnjuly1970 last updated on 28/Apr/21

You can't use 'macro parameter character #' in math mode

i f {(p q)}^{{s i n}^{2} (x)} + {(p q)}^{{c o s}^{2} (x)} = p + q

t h e n t a n (x) = ?

Answered by qaz last updated on 28/Apr/21

≪ 1 ≫: p = q = 0 \tan x = ? ? ?

≪ 2 ≫: p = q = 1 \tan x = ? ? ?

≪ 3 ≫: p, q \in (0, 1) \cup (1, \infty), p q \neq 1

{(p q)}^{\sin^{2} x} + {(p q)}^{\cos^{2} x}

= {(p q)}^{\sin^{2} x} + {(p q)}^{1 - \sin^{2} x} = p + q

\Rightarrow \sin^{2} x = {l o g}_{(p q)} p \cos^{2} x = {l o g}_{(p q)} q

o r \sin^{2} x = {l o g}_{(p q)} q \cos^{2} x = {l o g}_{(p q)} p

\tan x = \sqrt{{l o g}_{p} q} o r \sqrt{{l o g}_{q} p}

≪ 4 ≫: p, q \in C \tan x = ? ? ?

\dots . .

Facebook Tweet Pin