Answer:
Only statement (b) is correct.
[tex]\sin 35^{\circ} = \cos 55^{\circ}[/tex]
Step-by-step explanation:
Given certain trigonometric equality , we have to check which statements are true.
We know , [tex]\sin (90-\theta)=\cos \theta[/tex]
We will check each statement one by one,
Consider,
a) [tex]\sin 30^{\circ} = \cos 30^{\circ}[/tex]
We know from trigonometric table that ,
[tex]\sin 30^{\circ} =\frac{1}{2}[/tex] and [tex]\cos 30^{\circ}=\frac{\sqrt{3}}{2}[/tex]
Thus, [tex]\sin 30^{\circ} \neq \cos 30^{\circ}[/tex]
b) [tex]\sin 35^{\circ} = \cos 55^{\circ}[/tex]
Using above identity [tex]\sin (90-\theta)=\cos \theta[/tex]
[tex]\sin 35^{\circ} =\sin (90-55)^{\circ} =\cos55^{\circ} [/tex]
Thus, [tex]\sin 35^{\circ} = \cos 55^{\circ}[/tex]
c) [tex]\sin 60^{\circ} = \cos 60^{\circ}[/tex]
We know from trigonometric table that ,
[tex]\sin 60^{\circ} =\frac{\sqrt{3}}{2}[/tex] and [tex]\cos 30^{\circ}=\frac{1}{2}[/tex]
Thus, [tex]\sin 60^{\circ} \neq \cos 60^{\circ}[/tex]
d) [tex]\sin 55^{\circ} = \cos 25^{\circ}[/tex]
Using above identity [tex]\sin (90-\theta)=\cos \theta[/tex]
[tex]\sin 55^{\circ} =\sin (90-35)^{\circ} =\cos35^{\circ} [/tex]
Thus, [tex]\sin 55^{\circ} \neq\cos 25^{\circ}[/tex]
Thus, only statement (b) is correct.
