Question

Prove (sinA/2 ± cosA/2)² = 1± sinA

Answer 1

Step-by-step explanation:

(sinA/2 ± cosA/2)²

sin²A/2 + cos²A/2 ± 2sinA/2cosA/2

1 ± sin2(A/2)

1 ± sinA

Answer 2

Step-by-step explanation:

given

(sinA/2 ± cosA/2)² = 1± sinA

w.k.t

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

so

${ \sin( \frac{a}{2 } ) }^{2} + { \cos( \frac{a}{2} ) }^{2} \frac{ + }{ } 2 \sin( \binom{a}{2} ) \cos( \frac{a}{2} )$

so

$1 \frac{ + }{} \sin(2 \times \frac{a}{2} )$

so answer is

$1 \frac{ + }{} \sin(a)$

hence proved