if-7-sin-2-x-7-cos-2-x-8-find-x-

Question Number 211961 by Nadirhashim last updated on 25/Sep/24

i f 7^{{s i n}^{2} x} + 7^{{c o s}^{2} x} = 8 f i n d x

Answered by efronzo1 last updated on 25/Sep/24

7^{\sin^{2} x} = a \Rightarrow 7^{\cos^{2} x} = 7^{1 - \sin^{2} x} = \frac{7}{a}

\Rightarrow a + \frac{7}{a} = 8

\Rightarrow a^{2} - 8 a + 7 = 0

\Rightarrow a = 1 or a = 7

{\begin{cases} 7^{\sin^{2} x} = 1 \Rightarrow \sin^{2} x = 0 \\ 7^{\sin^{2} x} = 7 \Rightarrow \sin^{2} x = 1 \end{cases}

Answered by BaliramKumar last updated on 26/Sep/24

x = 0, \frac{π}{2}