Question

Can you please answer this question

Answer 1

`3tan^(2) \theta +7sec\theta=3`
First I converted the equation terms into sine and cosine.

`tan^(2)\theta = (sin^(2)\theta)/(cos^(2)\theta)` and
`sec\theta= (1)/(cos\theta)`
Substitution:

`(3sin^2\theta)/(cos^2\theta) + (7)/(cos\theta) =3`
Common Denominator Created:

`(3sin^2\theta)/(cos^2\theta) + (7cos\theta)/(cos^2\theta) =3`
Multiply each term by the LCD:

`3sin^2\theta+7cos\theta=3cos^2\theta`
Substitution: Recall ⇒
`sin^2\theta =1-cos^2\theta`

`3(1-cos^2\theta)+7cos\theta=3cos^2\theta`
Distribute and collect all terms on one side:

`6cos^2\theta-7cos\theta-3=0`
Factor and set each factor equal to 0:

`(2cos\theta-3)(3cos\theta+1)=0`

`2cos\theta-3=0`⇒
`theta=cos^(-1) (3)/(2)`

`3cos\theta+1=0`⇒
`theta=cos^(-1) (-1)/(3)`
The 2nd factor provides only possible answer 109.5 degrees