Question

Evalute (sin tita+cos tita)²-(sin tita-cos tita)²​

Answer 1

Solution:-

$\rm \to \: ( \sin \theta + \cos \theta) ^{2} - ( \sin \theta - \cos \theta)^{2}$

Using Identities

$\rm \to \: (a + b)^{2} = {a}^{2} + {b}^{2} + 2ab \\ \rm \to(a - b)^{2} = {a}^{2} + {b}^{2} - 2ab$

By using this identities

$\rm \to \: ( \sin {}^{2} \theta + \cos {}^{2} \theta + 2 \sin \theta \cos \theta) - (sin {}^{2} \theta + \cos {}^{2} \theta - 2 \sin \theta \cos \theta)$

Now using trigonometric identity

$\rm \to \: sin {}^{2} \theta + \cos {}^{2} \theta = 1$

$\rm \to \: 2 \sin \theta \cos \theta = \sin2 \theta$

We get

$\rm \to \: (1 + \sin2 \theta) - (1 - \sin2 \theta)$

$\rm \to \: 1 + \sin2 \theta - 1 + \sin 2\theta$

$\rm \to \: 2 \sin2\theta$

Answer

$\rm \to \: 2 \sin2\theta$