Question

if
5 sin A =
3, find the value of
sec² A-tan²A
cosec ²A - Cot²A
​

Answer 1

Answer:

5 sin A = 3

sin A = $\frac{opposite side}{hypotenuse}$ = $\frac{3}{5}$

by pythagoras theorem,

5² = 3² + x²

x² = 25 - 9

x² = 16

x = 4

i.  sec² A - tan² A

  $= (\frac{5}{4})^{2} - (\frac{3}{4} )^{2} \\= \frac{25 - 9}{16}\\= 1$

ii. cosec² A - cot² A

  $=( \frac{5}{3} )^{2} - (\frac{4}{3} )^2\\=\frac{25 - 16}{9} \\=1$