Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 58776 by George Mark Samuel last updated on 29/Apr/19

$${81}^{{sin}^{2}x}+{81}^{{cos}^{2}x}=30$$$$0⩽x⩽\pi .solveforx.$$

Answered by behi83417@gmail.com last updated on 29/Apr/19

$${81}^{{sin}^{2}x}+{81}^{1-{sin}^{2}x}=30\stackrel{{81}^{{\mathbf{sin}}^2\mathbf{x}}=\mathbf{t}}{\Rightarrow }$$$$\mathbf{t}+\frac{81}{\mathbf{t}}=30\Rightarrow {\mathbf{t}}^2-30\mathbf{t}+81=0\Rightarrow \mathbf{t}=3,27$$$$\Rightarrow \{\begin{array}{l}{81}^{{\mathbf{sin}}^2\mathbf{x}}=27\Rightarrow 4{\mathbf{sin}}^2\mathbf{x}=3\Rightarrow \mathbf{sinx}=\pm \frac{\sqrt{3}}{2}\\ {81}^{{\mathbf{sin}}^2\mathbf{x}}=3\Rightarrow 4{\mathbf{sin}}^2\mathbf{x}=1\Rightarrow \mathbf{sinx}=\pm \frac{1}{2}\end{array}$$$$\Rightarrow \{\begin{array}{l}\mathbf{sinx}=\pm \frac{\sqrt{3}}{2}\Rightarrow \mathbf{x}=2\mathbf{k}\mathit{\pi }+\frac{\mathit{\pi }}{3},2\mathbf{k}\mathit{\pi }+\frac{2\mathit{\pi }}{3}\\ \mathbf{sinx}=\pm \frac{1}{2}\Rightarrow \mathbf{x}=2\mathbf{k}\mathit{\pi }+\frac{\mathit{\pi }}{6},2\mathbf{k}\mathit{\pi }+\frac{5\mathit{\pi }}{6}\end{array}◼$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com