Question

y=(sinx/2+cosx/2)^2 at x=π/6

Answer 1

$\huge\boxed{\fcolorbox{cyan}{grey}{Solution:-}}$.

➡Given here.

↪y= (sin x/2 + Cosx/2)²,

= (sin²x/2 + Cos²x/2 +2sinx/2 cosx/2).

= 1+2sinx/2 Cosx/2.

= 1+sin2x/2.

= 1+sinx.

➡Keep , x=π/6.

↪y= 1+sinπ/6.

= 1+1/2.

= 1.5

➡Hopes ita helpa u

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Answer 2

Step-by-step explanation:

$y = {( \sin( \frac{x}{2}) + \cos( \frac{x}{2} ) ) }^{2} \: at \: x = \frac{\pi}{6} = > \\ y = {( \sin( \frac{\pi }{12} ) + \cos( \frac{\pi}{12} ) )}^{2} \\y = {( (\frac{ \sqrt{2 - \sqrt{3} } }{2}) + ( \frac{ \sqrt{2 + \sqrt{3} } }{2} ))}^{2} \\ \\(( {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab)) \\ \\ y = \frac{2 - \sqrt{3} }{4} + \frac{2 + \sqrt{3} }{4} + 2( \frac{2 - \sqrt{3} }{4} ) \\ y = 1 + \frac{2 - 2 \sqrt{3} }{4} \\ (y = \frac{ 6 - 2 \sqrt{3} }{4} ) \\ \\ therefore \: y = \frac{ 6 - 2 \sqrt{3} }{4} \: is \: the \: solution...$