Question

If tan53°=16/25,tan55°of value?

Answer 1

Answer:

$\huge\mathtt\blue{1/2}$

Step-by-step explanation:

(tan 13° tan 37° tan 45° tan 53° tan 77°)/[2 Cosec260°(Cos260°– 3cos 60° + 2)]

⇒ [tan(90° – 77°).tan(90° –  53°).tan45°.tan53°.tan77°)]/[2 Cosec260°(Cos260°– 3cos60° + 2)]

⇒ (cot77°.cot53° × 1 × tan 53° tan 77°)/[2 × 4/3 (1/4 – 3/2 + 2)

⇒ 1/[8/3 × 3/4]

⇒ 1/2

∴ The required value is 1/2

Answer 2

Answer:

25/16

Step-by-step explanation:

Correct Question :-

If tan35° = 16/25 , then the value of tan55°=?

Given,

tan35° = 16/25

To Find :-

Value of tan55°

Solution :-

We can write :-

35° = 90° - 55°

Applying 'tan' on both sides :-

tan35° = tan(90° - 55°)

tan35° = cot55°

[ tan(90° - A) = cotA]

16/25 = cot55°

16/25 = 1/tan55°

[ cotA = 1/tanA]

→ tan55° = 1/16/25

tan55° = 25/16