Question

If sec A = 5/4 verify that tanA/1+tan^2A= sinA/secA​

Answer 1

Solution:

We have been given , Sec A = 5/4

Find Value of tan A :

We know, Sec A = h/b

Using Pythagoras theorem to find the Base of right angled triangle:

H² = b² + p²

(5)² = ( 4)² + p²

25 = 16 + p²

25 - 16 = p²

p² = 9

p= 3

Verify given Equation:

tanA/1+tan^2A= sinA/secA

tanA / Sec²A = Sin A / 1/Cos A

tanA / Sec²A = Sin A × Cos A

3/4 ÷ 25/16 = 3/5 × 4/5

3/4 ÷ 15/16 = 12/25

3/4 × 16/15 = 12/25

12/25 = 12/25

Hence, It's Proved!