Year 12s: what will be the first way you research your future options? >>

C3 Trig

Hi, i ma having trouble with the questions below, if anyone could help that would be really useful. Is there an easy way to do them.....i find them really tricky! (i especially struggle on the proofs!) :confused:

1. Prove that tanθ +cotθ = 2 cosec 2θ

2. Solve by getting the exact answers in terms of π, 2(1- cos 2&#952 :wink:

= tan θ

3. Express sin^2θ in the form a + b cos 2θ, where a and b are constants.

4. Solve the equation 3 – 3 cos 2θ = 2 cosec θ, giving all solutions in radians in the interval 0 < θ < 2π

Thanks

Reply 1

nota bene

1. think about sin^2+cos^2 = 1 and sin2x=2sinxcosx... that made it possible for me to solve it...

Reply 2

Dez

Q1:

\displaystyle\huge \text{RHS} \equiv 2\csc 2\theta

\displaystyle\huge \equiv \frac{2}{\sin 2\theta}

\displaystyle\huge \equiv \frac{2}{2\sin \theta \cos \theta}

\displaystyle\huge \equiv \frac{1}{\sin \theta \cos \theta}

\displaystyle\huge \equiv \frac{\sin^2 \theta + \cos^2 \theta}{\sin \theta \cos \theta}

\displaystyle\huge \equiv \frac{\sin^2 \theta}{\sin \theta \cos \theta} + \frac{\cos^2 \theta}{\sin \theta \cos \theta}

\displaystyle\huge \equiv \frac{\sin \theta}{\cos \theta} + \frac{\cos \theta}{\sin \theta}

\displaystyle\huge \equiv \tan \theta + \cot \theta \equiv \text{LHS}

TSR's LaTeX system is crap... Those silly floating twos are supposed to be exponents, but for some reason decided they'd be happier riding on top of their trig functions instead of squaring them. :rolleyes:

Reply 3

zoopy

Dez

Q1:TSR's LaTeX system is crap... Those silly floating twos are supposed to be exponents, but for some reason decided they'd be happier riding on top of their trig functions instead of squaring them. :rolleyes:

Thanks a lot

Reply 4

zoopy

nota bene

1. think about sin^2+cos^2 = 1 and sin2x=2sinxcosx... that made it possible for me to solve it...