Name: Trigonometric Ratios of Complementary Angles
Uploaded: 2019-07-19
Duration: 9 min 3 s
Description: What is the connection between the trigonometric ratios of an angle and its complementary angle? This video not only gives you that but helps you derive them...

Question

Put $q = 0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}, 90^{\circ}$ in the given relations and check which value of $q$ satisfies these relations.

$\cos q + \sin q = \sqrt{2}$

Accepted Answer

Given:

$q = 0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}, 90^{\circ}$

$\cos q + \sin q = \sqrt{2}$

For $q = 0^{\circ},$

$\cos 0^{\circ} + \sin 0^{\circ} = \sqrt{2} 1 + 0 = \sqrt{2} 1 \neq \sqrt{2}$

Hence, $q = 0^{\circ}$ does not satisfy given relation.

For $q = 30^{\circ}$ ,

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

Hence, $q = 30^{\circ}$ does not satisfy given relation.

For $q = 45^{\circ}$ ,

$\cos 45^{\circ} + \sin 45^{\circ} = \sqrt{2} \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \sqrt{2} \frac{2}{\sqrt{2}} = \sqrt{2} 2 = \sqrt{2} \times \sqrt{2} 2 = 2$

Hence, $q = 45^{\circ}$ satisfies the given relation.

For $q = 60^{\circ}$ ,

$\cos 60^{\circ} + \sin 60^{\circ} = \sqrt{2} \frac{1}{2} + \frac{\sqrt{3}}{2} = \sqrt{2} \frac{1 + \sqrt{3}}{2} \neq \sqrt{2}$

Hence, $q = 60^{\circ}$ does not satisfy the given relation.

For $q = 90^{\circ}$ ,

$\cos 90^{\circ} + \sin 90^{\circ} = \sqrt{2} 0 + 1 = \sqrt{2} 1 \neq \sqrt{2}$

Hence, $q = 90^{\circ}$ does not satisfy the given relation.

Put $q = 0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}, 90^{\circ}$ in the given relations and check which value of $q$ satisfies these relations.

$\cos q + \sin q = \sqrt{2}$

Important Questions on Trigonometric Equation and Identities

Learn and Prepare for any exam you want !

Put q=0∘,30∘,45∘,60∘,90∘ in the given relations and check which value of q satisfies these relations. cosq+sinq=2

Important Questions on Trigonometric Equation and Identities

Learn and Prepare for any exam you want !

Put $q = 0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}, 90^{\circ}$ in the given relations and check which value of $q$ satisfies these relations.

$\cos q + \sin q = \sqrt{2}$