Question

Prove that the value 5 π/4 is a solution for the equation 3√2secθ + 7 = 1

Answer 1

`\bf sec(\theta)=\cfrac{1}{cos(\theta)}\\\\ -----------------------------\\\\ 3√(2)sec(\theta)+7=1\implies 3√(2)sec(\theta)=-6\implies sec(\theta)=\cfrac{-6}{3√(2)}\\\\ -----------------------------\\\\ now\qquad -\cfrac{6}{3√(2)}\implies -\cfrac{2}{√(2)}\implies -\cfrac{2}{√(2)}\cdot \cfrac{√(2)}{√(2)}\implies -\cfrac{2√(2)}{2}\implies -√(2)\\\\`


`\bf -----------------------------\\\\ \cfrac{1}{cos(\theta)}=-√(2)\implies \cfrac{1}{-√(2)}=cos(\theta)\\\\ -----------------------------\\\\ now\quad -\cfrac{1}{√(2)}\cdot \cfrac{√(2)}{√(2)}\implies -\cfrac{√(2)}{2}\\\\ -----------------------------\\\\ -\cfrac{√(2)}{2}=cos(\theta)\implies \theta= \begin{cases} (3\pi )/(4)\\\\ (5\pi )/(4) \end{cases}`