Question

To verify the identity 1-sin(theta)cos(theta)tan(theta)=cos^2(theta), a student subsituted theta =332. To the nearest hundredth, the value of each side of the identity was?

Answer 1

Please see below.

Explanation:

We have to prove :

`1-sinthetacosthetatantheta=cos^2theta`

We take LHS ,

`LHS=1-sinthetacosthetatantheta`

#LHS=1-sinthetacolor(violet)(cancelcolor(black) (costheta))*sintheta/color(violet)cancelcolor(black)(costheta)to[becausetanx=sinx/cosx]#

`LHS=1-sin^2theta`

`LHS=cos^2theta.....to[because cos^2x-sin^2x=1]`

`LHS=RHS`

If `theta=332^circ then`

`LHS=1-sin332^circcos332^circtan332^circ`

`LHS=1-(-0.47)(0.88)(-0.53)`

`LHS=1-0.22`

`LHS=0.78`

AND

`RHS=cos^2 332^circ`

`RHS=0.7795~~0.78`