Pre Calc Trig: Prove sinx(tan^2x+1)=tanxsecx; solve sinxcotx^2-sinxcsc^2 x=1/2

[hueyclemente]

Prove the following:

sinx(tan^2x+1)=tanxsecx


Find all solutions to the equation on [0,2π)

sinxcotx^2-sinxcsc^2 x=1/2

Thank you!

 

[JeffM]

This is a help site, not an answer site. Please show us your work so we can see where you need help.

Also, in the future, please post each problem in a separate threats.

 

[stapel]

1. Prove the following:

sinx(tan^2x+1)=tanxsecx

To learn how to prove trig identities, try here. Once you have learned the basic terms and techniques, please attempt the exercise. A good start might be to apply an identity to the parenthetical, and see where that leads.

2. Find all solutions to the equation on [0,2π)

sinxcotx^2-sinxcsc^2 x=1/2

To learn how to solve trig equations, please try here. Once you have studied the lesson, please attempt the exercise. A good first start might be to subtract the 1/2 over to the left-hand side, convert the cotangent and cosecant to sines and cosines, and multiply through to clear the denominators (remembering the note the restrictions on the domain, so that your solutions won't cause division-by-zero problems).

If you get stuck, please reply showing all of your work and reasoning so far. Thank you!