A simple trigonometrical equation.

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SUMMARY

The discussion centers on solving the trigonometric equation $$\cos(2\theta) = \left(\sqrt{2}+1\right)\left(\cos(\theta)-\frac{1}{\sqrt{2}}\right)$$. Participants recommend using the double-angle identity for cosine to transform the left side of the equation. Subsequently, the equation can be rewritten as a quadratic in terms of $$\cos(\theta)$$, allowing the application of the quadratic formula to find the values of $$\theta$$. This method provides a systematic approach to solving the equation.

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  • Understanding of trigonometric identities, specifically double-angle identities.
  • Familiarity with quadratic equations and the quadratic formula.
  • Basic knowledge of LaTeX for mathematical notation.
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  • Study the double-angle identity for cosine in detail.
  • Practice solving quadratic equations using the quadratic formula.
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vandana panchal
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If:

$$\cos(2\theta) = \left(\sqrt{2}+1\right)\left(\cos(\theta)-\frac{1}{\sqrt{2}}\right)$$

then what is the value of $\theta$?
 
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Hello vandana panchal, and welcome to MHB! :D

I wrapped your $\LaTeX$ code in MATH tags, so that it will be parsed correctly. I also made a few minor tweaks to the code.

For future reference, we do ask that our users show what they have tried so we know where you are stuck, and can offer better help.

To get you started, I think I would try a double-angle identity for cosine on the left, and then write the resulting quadratic in $\cos(\theta)$ in standard form, and apply the quadratic formula. What do you find?
 

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