ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios :
(i) sin 45°
(ii) cos 45°
(iii) tan 45°

Question

ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios : (i) sin 45° (ii) cos 45° (iii) tan 45°

KnowledgeBoat · Accepted Answer

In Δ ABC, ⇒ AC2 = BC2 \+ AB2 (∴ AC is hypotenuse) ⇒ AC2 = x2 \+ x2 ⇒ AC2 = 2x2 ⇒ AC = ⇒ AC = x As Δ ABC is isosceles right angled triangle, ∠BAC = ∠BCA = = 45° (i) sin 45° sin 45° = sin A = sin C sin A = = Hence, sin 45° = . (ii) cos 45° cos 45° = cos A = cos C cos A = = Hence, cos 45° = . (iii) tan 45° tan 45° = tan A = tan C tan A = = = 1 Hence, tan 45° = 1.

Mathematics

ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios :
(i) sin 45°
(ii) cos 45°
(iii) tan 45°

Trigonometric Identities

Related Questions

Prove that :
sin 60° = 2 sin 30° cos 30°.

Prove that :
4 (sin⁴ 30° + cos⁴ 60°) - 3 (cos² 45° - sin² 90°) = 2

Mathematics

ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios :(i) sin 45°(ii) cos 45°(iii) tan 45°

Trigonometric Identities

Related Questions

Prove that :sin 60° = 2 sin 30° cos 30°.

Prove that :4 (sin4 30° + cos4 60°) - 3 (cos2 45° - sin2 90°) = 2

ABC is an isosceles right-angled triangle. Assuming AB = BC = x, find the value of each of the following trigonometric ratios :
(i) sin 45°
(ii) cos 45°
(iii) tan 45°

Prove that :
sin 60° = 2 sin 30° cos 30°.

Prove that :
4 (sin⁴ 30° + cos⁴ 60°) - 3 (cos² 45° - sin² 90°) = 2