Trig problems (1 Viewer)

[capper]

I need help with these questions

Find the general solution to the following equations

1. tan a = sin2a
2. cosx - sinx =1
3. sin4x - sin2x =0
4. cos 3a = cos a
5. 3tan 2a =2tan a

Also does anyone know a good latex website that has the square and cube root for equations
Thanks

 

[hayabusaboston]

My comment was removed..? I didn't do anything wrong....

One learns most from doing it by oneself

 

[Carrotsticks]

I won't give you the full solution, but I'll tell you how to start:

1. Turn the tanA into sinA/cosA and turn the sin2A into 2sinAcosA.

2. Use auxiliary angles to convert into the form Rsin(x-a), then solve. OR divide all terms by cosX then square both sides, and use one of the Pythagorean Identities to simplify and solve it. OR you can square both sides directly and use a combination of a Pythagorean Identity and Double Angle formulae to solve.

3. Turn the sin4X into 2sin2Xcos2X, then solve.

4. Fully expand the cos3A into an expression in terms of powers of cosA, then solve.

5. Turn the tan2A into an expression in terms of tanA (double angle formula) and then solve.

 

[capper]

just want to know how to do question 2 because i dont know how to do it

 

[Carrotsticks]

just want to know how to do question 2 because i dont know how to do it

The third way (dividing both sides by cos(x) ) is very long unnecessarily, but it is a method nonetheless).