Question

2. sin4teta - cos4teta /
sinsquare teta - cos²o =
a)-1 b) 2
c) 0

d) 1​

Answer 1

The required "option (d) 1" is correct.

Step-by-step explanation:

We have,

$\dfrac{\sin^{4}\theta - \cos^{4}\theta}{\sin^{2}\theta - \cos^{2}\theta}$

=$\dfrac{(\sin^{2}\theta + \cos^{2}\theta)(\sin^{2}\theta - \cos^{2}\theta)}{\sin^{2}\theta - \cos^{2}\theta}$

[∵ $a^{2} -b^{2} =(a+b)(a-b)$ ]

$=\sin^{2}\theta + \cos^{2}\theta$

= 1

[ ∵ $sin^{2}\theta + \cos^{2}\theta = 1$]

Hence, the required "option (d) 1" is correct.