MCQ
જો $\sin (\pi\cos\theta)=\cos(\pi\sin\theta),$ તો $\cos\left(\pi+\frac{\pi}{4}\right)$ નું મૂલ્ય ............
- A$-\frac{1}{2\sqrt{2}}$
- ✓$\frac{1}{2\sqrt{2}}$
- C$\frac{2}{\sqrt{2}}$
- D$\frac{1}{\sqrt{2}}$
$\sin(\pi\cos\theta)=\cos(\pi\sin\theta)$
$\therefore\sin(\pi\cos\theta)=\sin\left(\frac{\pi}{2}+\pi\sin\theta\right)$
$\therefore \pi\cos\theta=\frac{\pi}{2}+\sin\theta\pi$
$\therefore (\cos\theta-\sin\theta)\pi=\frac{\pi}{2}$
$\therefore \cos\theta-\sin\theta=\frac{1}{2}$
$\therefore \cos\left(\theta+\frac{\pi}{4}\right)=\frac{1}{2\sqrt{2}}$
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| $X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
| $f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
નુંવિચરણ જો $160$ હોય તો $\mathrm{c} \in \mathrm{N}$ નું મૂલ્ય ............ છે.