Answer:
1 ) sin 165°
2 ) cos 330°
3 ) Tan 157.5°
4 ) [tex]sin^2 157.5[/tex]
Step-by-step explanation:
1 )
Given expression is [tex]\sqrt{\frac{1-cos330}{2} }[/tex]
We know that [tex]cos2x=1-2sinx^{2}[/tex]
[tex]sinx^{2}=\frac{1-cos2x}{2}[/tex]
[tex](sinx/2)^2=\frac{1-cosx}{2}[/tex]
So the first expression is sin (330/2)° =sin 165°
2 )
GIven expression is [tex]1-2sin^2165[/tex]
We know that [tex]cos2x=1-2sinx^{2}[/tex]
So the result is cos 330°
3 )
Given expression is [tex]\frac{1-cos 315}{sin315}[/tex]
We know that [tex]cos2x=1-2sinx^{2}[/tex]
Also we know that sin2x = 2sinxcosx
So The numerator becomes [tex]2sin^2x/2[/tex]. and the denominator becomes as [tex]2sinx/2cosx/2[/tex]
[tex]\frac{2sin^2x/2}{2sinx/2cosx/2}=tanx/2[/tex]
So the result is Tan 157.5°
4 )
Given expression is [tex]\frac{1-cos 315}{2}[/tex]
We know that [tex]cos2x=1-2sinx^{2}[/tex]
[tex](sinx/2)^2=\frac{1-cosx}{2}[/tex]
So the result is [tex]sin^2 157.5[/tex]
