Question

If 11x is an acute angle and tan 11x = cot 7x, then what is the value of x?

(a) 5°

(b) 6°

(c) 7°

(d) 8°

Answer 1

Correct option is (a) 5°

tan11x = cot7x

⇒ tan11x = tan(90° − 7x)

⇒ tan11x − tan(90° − 7x) = 0

⇒ tan(11x − 90° + 7x) (1 + tan11x.tan(90° − 7x)) = 0

⇒ tan(18x − 90°) (1 + tan11x.tan(90° − 7x)) = 0

⇒ tan(18x − 90°) = 0  [\(\because\) 1 + tan11x.tan(90 °− 7x) \(\ne\) 0]

⇒ tan(10x − 90°) = tan0°

⇒ 18x − 90° = 0

⇒ 18x = 90°

⇒ x = 5°