Question

$cot^4A-cot^2A=1$ হলে, প্রমাণ কর যে, $cos^4A+cos^2A=1$

Answer 1

দেওয়া আছে,
$cot^4A-cot^2A=1$

বা, $cot^4A=1+cot^2A$

বা, $cot^4A=cosec^2A$

বা, $\frac{\cos^4A}{\sin^4A}=\frac1{\sin^2A}$

বা, $\frac{\cos^4A}1=\frac{\sin^4A}{\sin^2A}$

বা, $\cos^4A=\sin^2A$

বা, $\cos^4A=1-\cos^2A$

$\therefore \cos^4A+\cos^2A=1$ [Proved]

Comments

Rules Applied :

• $cosec^2\theta=1+cot^2\theta$
• $cot\theta=\frac{cos\theta}{sin\theta}$
• $cosec\theta=\frac{1}{cos\theta}$
• $sin^2\theta=1-cos^2\theta$