Question

Consider the following statements:

1. The value of cos 61° + sin 29° cannot exceed 1.

2. The value of tan 23° - cot 67° is less than 0.

Which of the above statements is / are correct?

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

Answer 1

Correct Answer - Option 1 : 1 only

Concept used :

cos (90° - θ) = sin θ

tan (90° - θ) = cot θ  

Calculations :

Statement 1 

cos 61° + sin 29° = sin 29° + sin 29° 

⇒ 2 sin 29° 

⇒ 2 sin 29° < 1     (sin 29° is less than 0.5 as the value of sin θ increases from 0° to 90° and the value of sin 30° is 0.5)

Statement 2 

tan 23° - cot 67° = cot 67° - cot 67° 

⇒ 0  

Only statement 1 is correct 

∴ Option 1 is the correct choice.