Question

If 13 Sin A = 5 tan A, find the value of sec² A − tan² A

Answer 1

Step-by-step explanation:

sinA sinA 5

____ = ________ = __

tanA sinA÷cosA 13

cosA = 5/13, sinA = x/13

x²+5² = 13²

x²+25 = 169

x² = 144 = 12²

secA = 1/ cosA = 13/5

Sec²A = 13²/5²= 169/25

tanA = sinA/cosA = 12/5

tan²A = 12²/5² = 144/25

sec²A - tan²A = 169/25 - 144/ 25

= 169-144/25 = 25/25 =1