Prove that : cos2 30° - sin2 30° = cos 60°

cos2 30° - sin2 30° = cos 60° L.H.S. = cos2 30° - sin2 30° R.H.S.. = cos 60° = ∴ L.H.S. = R.H.S. Hence proved, cos2 30° - sin2 30° = cos 60°.

Mathematics

Prove that :
cos² 30° - sin² 30° = cos 60°

Trigonometric Identities

12 Likes

Answer

cos² 30° - sin² 30° = cos 60°

L.H.S. = cos² 30° - sin² 30°

$= \Big(\dfrac{\sqrt3}{4}\Big)^2 - \Big(\dfrac{1}{4}\Big)^2 \\[1em] = \dfrac{3}{4} - \dfrac{1}{4}\\[1em] = \dfrac{3 - 1}{4}\\[1em] = \dfrac{2}{4}\\[1em] = \dfrac{1}{2}$

R.H.S.. = cos 60° = $\dfrac{1}{2}$

∴ L.H.S. = R.H.S.

Hence proved, cos² 30° - sin² 30° = cos 60°.

Answered By

4 Likes

Mathematics

Prove that :
cos² 30° - sin² 30° = cos 60°

Trigonometric Identities

Answer

Related Questions

Prove that :
cos 30°. cos 60° - sin 30°. sin 60° = 0

Prove that :
cosec² 45° - cot² 45° = 1

Prove that :
$\Big(\dfrac{\text{tan 60° + 1}}{\text{tan 60° - 1}}\Big)^2 = \dfrac{\text{1 + cos 30°}}{\text{1 - cos 30°}}$

Prove that :
3 cosec² 60° - 2 cot² 30° + sec² 45° = 0.

Mathematics

Prove that :cos2 30° - sin2 30° = cos 60°

Trigonometric Identities

Answer

Related Questions

Prove that :cos 30°. cos 60° - sin 30°. sin 60° = 0

Prove that :cosec2 45° - cot2 45° = 1

Prove that :(tan 60° + 1tan 60° - 1)2=1 + cos 30°1 - cos 30°\Big(\dfrac{\text{tan 60° + 1}}{\text{tan 60° - 1}}\Big)^2 = \dfrac{\text{1 + cos 30°}}{\text{1 - cos 30°}}(tan 60° - 1tan 60° + 1​)2=1 - cos 30°1 + cos 30°​

Prove that :3 cosec2 60° - 2 cot2 30° + sec2 45° = 0.

Prove that :
cos² 30° - sin² 30° = cos 60°

Prove that :
cos 30°. cos 60° - sin 30°. sin 60° = 0

Prove that :
cosec² 45° - cot² 45° = 1

Prove that :
$\Big(\dfrac{\text{tan 60° + 1}}{\text{tan 60° - 1}}\Big)^2 = \dfrac{\text{1 + cos 30°}}{\text{1 - cos 30°}}$

Prove that :
3 cosec² 60° - 2 cot² 30° + sec² 45° = 0.