How do you solve 4\sec ^{2}\Theta =5 ?

2 Answers
Nov 4, 2017

theta = 26.5 degree

Explanation:

sec^2 theta = 5/4
cos^2theta = 4/5

Now

(1+cos2theta)/2 = cos^2theta

Therefore,

(1+cos2theta)/2 = 4/5
(1+cos2theta) = 8/5

Rearranging it

cos2theta=3/5

therefore

cos2theta=cos53 degree

that means

2theta = 53 degree

theta = 26.5 degree

Nov 4, 2017

26.57^o

Explanation:

Using identity:

sec^2theta= 1 + tan^2theta

4(1+tan^2theta)=5

4+4tan^2theta=5

tan^2theta=1/4

tantheta= sqrt(1/4)=1/2

theta= arctan(tantheta) = arctan(1/2)=26.57^o ( 2 .d.p )