Evaluate the following : 2 x [(cos² 20° + cos² 70°) / (sin² 25° + sin² 65°)] - tan 45° + tan 13° tan 23° tan 30° tan 67° tan 77°

Question

KnowledgeBoat · Accepted Answer

Since, angles are acute in the equation, ∴ cos(90° - θ) = sin θ, sin(90° - θ) = cos θ and tan(90° - θ) = cot θ. Using above equations in 2 x - tan 45° + tan 13° tan 23° tan 30° tan 67° tan 77° = 2 x - tan 45° + tan 13° tan 23° tan 30° tan (90 - 23)° tan (90 - 13)° = 2 x - tan 45° + tan 13° tan 23° tan 30° cot 23° cot 13° = 2 x 1 - 1 + tan 13° cot 13° tan 23° cot 23° tan 30° = 1 + 1 x = = = . Hence, the value of the expression is .

Mathematics

Evaluate the following : 2 x [(cos² 20° + cos² 70°) / (sin² 25° + sin² 65°)] - tan 45° + tan 13° tan 23° tan 30° tan 67° tan 77°

Trigonometric Identities

Related Questions