Final answer to the problem
$\cos\left(x\right)=\sqrt{\frac{3}{2}},\:\cos\left(x\right)=-\sqrt{\frac{3}{2}}\:,\:\:n\in\Z$
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Step-by-step Solution
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- Express in terms of sine and cosine
- Simplify
- Simplify into a single function
- Express in terms of Sine
- Express in terms of Cosine
- Express in terms of Tangent
- Express in terms of Cotangent
- Express in terms of Secant
- Express in terms of Cosecant
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1
Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$
Learn how to solve trigonometric equations problems step by step online.
$2\sin\left(x\right)+\frac{1}{\sin\left(x\right)}=0$
Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation 2sin(x)+csc(x)=0. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Combine all terms into a single fraction with \sin\left(x\right) as common denominator. Multiply both sides of the equation by \sin\left(x\right). Applying the trigonometric identity: \sin\left(\theta \right)^2 = 1-\cos\left(\theta \right)^2.
Final answer to the problem
$\cos\left(x\right)=\sqrt{\frac{3}{2}},\:\cos\left(x\right)=-\sqrt{\frac{3}{2}}\:,\:\:n\in\Z$
