Question

Q5 to prove please tell th answer of this

Answer 1

$use \: \: the \: \: identity \\ {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ {(1 - \sin \theta + \cos\theta) }^{2} = {1}^{2} + { \sin }^{2} \theta + { \cos }^{2} \theta + 2(1 \times - \sin\theta - \sin\theta \times \cos \theta + \cos\theta \times 1) \\ = 1 + 1 + 2( - \sin\theta - \sin\theta \cos \theta + \cos\theta) \\ = 2+ 2( - \sin\theta - \sin\theta \cos \theta + \cos\theta) \\ = 2(1 - \sin\theta - \sin\theta \cos \theta + \cos\theta) \\ = 2(1 - \sin\theta + \cos \theta (1 - \sin\theta) ) \\ = 2 (1 - \sin\theta) (1 + \cos\theta)$