find the exact value of the expression:
6tan^2(π/4)+18sec^2(π/4).
well, you should of course know that
tan(π/4) = 1
sec(π/4) = √2
and now you just plug and chug.
π/4 radians = 45°
you should know that tan45° = 1 and cos45° = 1/√2
so cos^2 45° = 1/2, which would make sec^2 45° = 2
take over
To find the exact value of the expression 6tan^2(π/4) + 18sec^2(π/4), we need to know the trigonometric identities for tangent (tan) and secant (sec), as well as the value of π/4.
First, let's recall the values of tangent and secant for π/4:
tan(π/4) = 1
sec(π/4) = 1
Using these values, let's substitute them into the given expression:
6tan^2(π/4) + 18sec^2(π/4)
= 6(1)^2 + 18(1)^2
= 6(1) + 18(1)
= 6 + 18
= 24
Therefore, the exact value of the expression 6tan^2(π/4) + 18sec^2(π/4) is 24.