Topic: Math Verify: (cos^2x)(tan^2x) + (cos^2x)= 1 Thank you in advance....

2 Answers

jeew-m's profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

In trigonometry there is a major trigonometric identity as;

`sin^2x+cos^2x = 1`


We also know that;

`tanx = (sinx)/cosx`


Now we will start the question from Left Hand Side(LHS)


`= (cos^2x)tan^2x+cos^2x`

`= (cos^2x)(sin^2x)/(cos^2x)+cos^2x`

`= sin^2x+cos^2x`

`= 1`

`= RHS`


So it is proven that `(cos^2x)tan^2x+cos^2x = 1`


embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

Show `cos^2x(tan^2x)+cos^2x=1` :

`cos^2x(tan^2x)+cos^2x`   Given

`=cos^2x(tan^2x+1)`  Factor out common term

`=cos^2x(sec^2x)` Pythasgorean relationship

`=cos^2x*1/(cos^2x)`  Definition of sec(x)

`=1` as required.