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

Question

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

KnowledgeBoat · Accepted Answer

Solving, ⇒ sin² 34° + sin² 56° + 2 tan 18° tan 72° - cot² 30° ⇒ sin² 34° + sin² (90° - 34°) + 2 tan (90° - 72°) tan 72° - cot² 30° We know that, sin (90° - θ) = cos θ, cos (90° - θ) = sin θ and tan (90° - θ) = cot θ ⇒ sin² 34° + cos² 34° + 2 cot 72° tan 72° - cot² 30° As, cot θ. tan θ = 1 and sin² θ + cos² θ = 1. ⇒ 1 + 2 - ⇒ 3 - 3 ⇒ 0. Hence, sin² 34° + sin² 56° + 2 tan 18° tan 72° - cot² 30 = 0.

Mathematics

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

Trigonometrical Ratios

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Mathematics

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

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

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