Question

Value of cos⁡(−1230∘)×cot⁡(−315∘) is:

• A. (A) −32
• B. (B) 23
• C. (C) 12
• D. (D) −12

Answer 1

Answer: (A)

(A) −32

Answer 2

Explanation:
Given:cos⁡(−1230∘)×cot⁡(−315∘)Concept:cos⁡(−θ)=cos⁡θcos⁡(2nπ+θ)=cos⁡(θ)cos⁡(π−θ)=−cos⁡(θ)cot⁡(−θ)=−cot⁡(θ)cot⁡(2nπ−θ)=−cot⁡(θ)According to the ques,cos⁡(−1230∘)=cos⁡(1230∘)(∵cos⁡(−θ)=cos⁡θ)=cos⁡(3×360∘+150)(∵cot⁡(2nπ−θ)=−cot⁡(θ))=cos⁡(150∘)=cos⁡(180∘−30∘)=−cos⁡30∘(∵cos⁡(π−θ)=−cos⁡(θ))=−32Now,cot⁡(−315∘)=−cot⁡(315∘)(∵cot⁡(−θ)=−cot⁡(θ))=−cot⁡(360∘−45∘)=cot⁡45∘(∵cot⁡(2nπ−θ)=−cot⁡(θ))=1cos⁡(−1230∘)×cot⁡(−315∘)=−32Hence, the correct option is (A).