Question

If tan (x² – 8x + 60)° = cot (6x – 5)°, what is one of the values of x?

(a) 7 

(b) 8 

(c) 9 

(d) 10.

Answer 1

(a) 7

tan (x² – 8x + 60)° = cot (6x – 5)° 

⇒ tan (x² – 8x + 60)° = tan [90 – (6x – 5)]° 

⇒ (x² – 8x + 60)° = 90° – (6x – 5)° 

⇒ x² – 8x + 60 = 90 – 6x + 5 ⇒ x² – 2x – 35 = 0 

⇒ (x – 7) (x + 5) = 0 ⇒ x = 7, –5 ⇒ x = 7