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  4. The most general value of θ, satisfying the two equations, cos θ = (1/√2) , tan θ = 1 is :

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Q. The most general value of $\theta$, satisfying the two equations, $\cos \theta = \frac{1}{\sqrt{2}} , \tan \, \theta = 1$ is :

Trigonometric Functions

Solution:

The values of $\theta$ lying between 0 and $2 \pi$ and satisfying the given equations is $\theta = \frac{5 \pi}{4}$.
Hence, the general value of $\theta$ satisfying the given equation is
$ \theta = 2 n \pi + \frac{5 \pi}{4} \, \Rightarrow \, \theta = (2 n + 1) \pi + \frac{\pi}{4}$