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 $\displaystyle \cos (2 \theta) = 1 - 2 \sin^2 (\theta )$ and re-arrange to get the quadratic equation $\displaystyle 4 \sin^2 \theta + 7 \sin \theta - 2 = 0$.
Solve for $\displaystyle \sin \theta$ and then solve for $\displaystyle \theta$.
2. Work with the left hand side: Substitute $\displaystyle \tan \theta = \frac{\sin \theta}{\cos \theta}$. Multiply numerator and denominator by $\displaystyle \cos^2 \theta$. Simplify the numerator and denominator using standard identities to get the right hand side.
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