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

4 (sin4 30° + cos4 60°) - 3 (cos2 45° - sin2 90°) = 2 L.H.S. = 4 (sin4 30° + cos4 60°) - 3 (cos2 45° - sin2 90°) R.H.S. = 2 ∴ L.H.S. = R.H.S. Hence, 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°

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

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If sin x = cos x and x is acute, state the value of x.

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If sec A = cosec A and 0° ≤ A ≤ 90°, state the value of A.

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Mathematics

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

Trigonometric Identities

Related Questions

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°.

If sin x = cos x and x is acute, state the value of x.

If sec A = cosec A and 0° ≤ A ≤ 90°, state the value of A.

Mathematics

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

Trigonometric Identities

Related Questions

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°.

If sin x = cos x and x is acute, state the value of x.

If sec A = cosec A and 0° ≤ A ≤ 90°, state the value of A.

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°.