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3 years ago

15

Solve Sec 5theta/4=2

1 answer:

nignag [31]3 years ago

3 0

$\sec\dfrac{5\theta}{4}=2\\
\dfrac{1}{\cos \dfrac{5\theta}{4}}=2\\
\cos \dfrac{5\theta}{4}=\dfrac{1}{2}\\
 \dfrac{5\theta}{4}=\dfrac{\pi}{3}+2k\pi \vee \dfrac{5\theta}{4}=-\dfrac{\pi}{3}+2k\pi\\
5\theta=\dfrac{4\pi}{3}+8k\pi \vee 5\theta=-\dfrac{4\pi}{3}+8k\pi\\
\boxed{\theta=\dfrac{4\pi}{15}+\dfrac{8k\pi}{5} \vee \theta=-\dfrac{4\pi}{15}+\dfrac{8k\pi}{5}}$

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