More Trigonometric Identities?

Question

9(sex^2 (x)) - 5(tan^2 (x)) = 5 + 4(sec^2 (x))

ALSO:

What does it mean when a number (in the case above we have 9, -5 and 4) is written IN FRONT of trig identities?

Answer 1

Prove the identity. I assume you mean:

9sec²x - 5tan²x = 5 + 4sec²x

Let's start with the left hand side.
_________

Left Hand Side = 9sec²x - 5tan²x = 9/cos²x - 5sin²x/cos²x

= (4 + 5 - 5sin²x)/cos²x = (4 + 5cos²x)/cos²x

= (5cos²x + 4)/cos²x

= 5 + 4/cos²x = 5 + 4sec²x = Right Hand Side

Answer 2

we should multiply the numbers in front with the trig identities