MHB A simple trigonometrical equation.

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The discussion revolves around solving the trigonometric equation cos(2θ) = (√2 + 1)(cos(θ) - 1/√2). Participants suggest using a double-angle identity for cosine to simplify the left side of the equation. The next step involves rewriting the resulting expression as a quadratic equation in terms of cos(θ). Applying the quadratic formula is recommended to find the values of θ. The conversation emphasizes the importance of showing previous attempts to facilitate better assistance.
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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