Question

সমাধান কর: $sin \theta + cos \theta =1$, যখন $0^\circ \leq \theta \leq 90^\circ$

Answer 1

প্রদত্ত সমীকরণ,
$sin \theta + cos \theta =1$

বা, $\left(sin \theta + cos \theta \right)^2 = (1)^2$

বা, $sin^2\theta + 2 \cdot sin\theta \cdot cos\theta + cos^2\theta = 1$

বা, $sin^2\theta + cos^2\theta + 2 \cdot sin\theta \cdot cos\theta= 1$

বা, $1 + 2 \cdot sin\theta \cdot cos\theta= 1$

বা, $2 \cdot sin\theta \cdot cos\theta= 1-1$

বা, $2 \cdot sin\theta \cdot cos\theta= 0$

বা, $sin\theta \cdot cos\theta= \frac{0}{2}$

বা, $sin\theta \cdot cos\theta= 0$

এখন, হয়,
$sin\theta= 0$

বা, $sin\theta= sin0^\circ$

$\therefore \theta= 0^\circ$

অথবা,
$cos\theta= 0$

বা, $cos\theta= cos90^\circ$

$\therefore \theta= 90^\circ$

$\therefore$ $\theta$ এর মান $0^\circ$ অথবা, $90^\circ$ [Answer]