1. ## Double Angle

hi i am really struggling with these 2 questions and any help would be deeply appreciated.

1. 2cos 2theta= 7 sintheta solve for 0<theta<2 pi, answer to one decimal

2. prove that
1 - tan squared theta / 1 + tan squared theta = cos 2 theata

2. Originally Posted by brooksy
hi i am really struggling with these 2 questions and any help would be deeply appreciated.

1. 2cos 2theta= 7 sintheta solve for 0<theta<2 pi, answer to one decimal

2. prove that
1 - tan squared theta / 1 + tan squared theta = cos 2 theata
1. Substitute $\cos (2 \theta) = 1 - 2 \sin^2 (\theta )$ and re-arrange to get the quadratic equation $4 \sin^2 \theta + 7 \sin \theta - 2 = 0$.
Solve for $\sin \theta$ and then solve for $\theta$.

2. Work with the left hand side: Substitute $\tan \theta = \frac{\sin \theta}{\cos \theta}$. Multiply numerator and denominator by $\cos^2 \theta$. Simplify the numerator and denominator using standard identities to get the right hand side.

3. thanks for that but im still really struggling to get the final answer.
for 1. i've got to 4sinsquared theta + 7 sin theta -2=0 do i then factorise or what.

2.ive mulitplied by cos squared theta and got
cos squared theta - sin squared theta / cos squared theta + sin squared theta. not sure what to do next

4. Originally Posted by brooksy
thanks for that but im still really struggling to get the final answer.
for 1. i've got to 4sinsquared theta + 7 sin theta -2=0 do i then factorise or what. Mr F says: Yes. Or use the quadratic formula to solve for ${\color{red}sin \theta}$. Only one of the solutions for ${\color{red}sin \theta}$ will be valid.

2.ive mulitplied by cos squared theta and got
cos squared theta - sin squared theta / cos squared theta + sin squared theta. not sure what to do next Mr F says: Surely you're familar with the double angle formulae and the Pythagorean Identity.
I doubt very much that 9 minutes (the time between post #2 and post #3) is sufficient time to engage with the questions using the suggestions I made in post #2.

5. thanks for the help Mr F