KnowledgeBoat Logo

Mathematics

Without using trigonometric tables, evaluate the following:

tan 41°cot 49°\dfrac{\text{tan 41°}}{\text{cot 49°}}

Trigonometrical Ratios

32 Likes

Answer

(ii) Solving,

⇒tan 41°cot 49°⇒tan (90° - 49°)cot 49°As, tan (90 - θ) = cot θ⇒cot 49°cot 49°⇒1.\Rightarrow \dfrac{\text{tan 41°}}{\text{cot 49°}} \\[1em] \Rightarrow \dfrac{\text{tan (90° - 49°)}}{\text{cot 49°}} \\[1em] \text{As, tan (90 - θ) = cot θ} \\[1em] \Rightarrow \dfrac{\text{cot 49°}}{\text{cot 49°}} \\[1em] \Rightarrow 1.

Hence, tan 41°cot 49°=1\dfrac{\text{tan 41°}}{\text{cot 49°}} = 1.

Answered By

9 Likes

Related Questions