sin² 34° + sin² 56° + 2 tan 18° tan 72° - cot² 30°

Question

KnowledgeBoat · Accepted Answer

We need to find the value of: sin² 34° + sin² 56° + 2 tan 18° tan 72° - cot² 30° The above equation can be written as, sin² 34° + sin² (90 - 34)° + 2 tan 18° tan (90 - 18)° - cot² 30°. As, sin(90 - θ) = cos θ, tan(90 - θ) = cot θ, sin²θ + cos²θ = 1, tan θ.cot θ = 1 and cot 30° = . Using in above equation we get, ⇒ sin² 34° + cos² 34° + 2 tan 18° cot 18° - ⇒ 1 + 2 - 3 = 0. Hence, the value of the above expression is 0.

Mathematics

Without using trigonometric tables, evaluate the following:
sin² 34° + sin² 56° + 2 tan 18° tan 72° - cot² 30°.

Trigonometric Identities

Related Questions

Without using trigonometric tables, evaluate the following:
(cos² 25° + cos² 65°) + cosec θ sec(90° - θ) - cot θ tan (90° - θ).

Mathematics

Without using trigonometric tables, evaluate the following:sin2 34° + sin2 56° + 2 tan 18° tan 72° - cot2 30°.

Trigonometric Identities

Related Questions

Without using trigonometric tables, evaluate the following:(cos2 25° + cos2 65°) + cosec θ sec(90° - θ) - cot θ tan (90° - θ).

Without using trigonometric tables, evaluate the following:
sin² 34° + sin² 56° + 2 tan 18° tan 72° - cot² 30°.

Without using trigonometric tables, evaluate the following:
(cos² 25° + cos² 65°) + cosec θ sec(90° - θ) - cot θ tan (90° - θ).