Question

Which of the following statements is true? a. sin 30° = cos 30° b. sin 35° = cos 55° c. sin 60° = cos 60° d. sin 55° = cos 25°

Answer 1

Answer:

Only statement (b) is correct.

$\sin 35^{\circ} = \cos 55^{\circ}$

Step-by-step explanation:

Given certain trigonometric equality , we have to check which statements are true.

We know , $\sin (90-\theta)=\cos \theta$

We will check each statement one by one,

Consider,

a) $\sin 30^{\circ} = \cos 30^{\circ}$

We know from trigonometric table that ,

$\sin 30^{\circ} =\frac{1}{2}$ and  $\cos 30^{\circ}=\frac{\sqrt{3}}{2}$

Thus, $\sin 30^{\circ} \neq \cos 30^{\circ}$

b) $\sin 35^{\circ} = \cos 55^{\circ}$

Using above identity $\sin (90-\theta)=\cos \theta$

$\sin 35^{\circ} =\sin (90-55)^{\circ} =\cos55^{\circ}$

Thus, $\sin 35^{\circ} = \cos 55^{\circ}$

c) $\sin 60^{\circ} = \cos 60^{\circ}$

We know from trigonometric table that ,

$\sin 60^{\circ} =\frac{\sqrt{3}}{2}$ and  $\cos 30^{\circ}=\frac{1}{2}$

Thus, $\sin 60^{\circ} \neq \cos 60^{\circ}$

d) $\sin 55^{\circ} = \cos 25^{\circ}$

Using above identity $\sin (90-\theta)=\cos \theta$

$\sin 55^{\circ} =\sin (90-35)^{\circ} =\cos35^{\circ}$

Thus, $\sin 55^{\circ} \neq\cos 25^{\circ}$

Thus, only statement (b) is correct.

Answer 2

b. sin 35° = cos 55° is the correct answer i believe :)