Question

if cosx=2/3, find the value of 2sec^2x+tan^2x-7.​

Answer 1

Answer:

-5/4

Step-by-step explanation:

cosx=2/3

cosx=Base/Hypotenuse

Therefore Base=2k and Hypotenuse=3k

Therefore Using pythagoras theorem

we get (P)^2=(H)^2-(B)^2

(P)^2=(3k)^2-(2k)^2

(P)^2=9k^2-4k^2

(P)^2=5k^2

P=sqrt{5} k

secx=3/2

tanx=sqrt{5}/2

therefore 2*(3/2)^2+(sqrt{5})^2-7

18/4+5/4-7

23/4-28/4

=-5/4

sqrt=Square root

^= to the power