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

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

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

Exam Questions HH]elp

I need some help with these exam questions. Struggling with the proof of trig identities.

Thanks. :smile:

:smile:

https://www.dropbox.com/sh/q829c1wi86mazt7/AACHOgK4NIDFS-UWMwqF8Ra1a?dl=0

Study Forum Helper

Original post by Jeevs090909

I need some help with these exam questions. Struggling with the proof of trig identities.

Thanks. :smile:

:smile:

https://www.dropbox.com/sh/q829c1wi86mazt7/AACHOgK4NIDFS-UWMwqF8Ra1a?dl=0

\displaystyle \mathrm{cosec \ } x \equiv \sec x + \frac{2 \cot 2x}{\sin x + \cos x}

Start with the RHS. Express everything in terms of sin and cos, then get it under the same denominator.

OP

Original post by RDKGames

\displaystyle \mathrm{cosec \ } x \equiv \sec x + \frac{2 \cot 2x}{\sin x + \cos x}

Start with the RHS. Express everything in terms of sin and cos, then get it under the same denominator.

Thanks

:smile:

Study Forum Helper

Original post by Jeevs090909

Thanks

:smile:

For the circle question, you simply need to get it in the form

(x-a)^2+(y-b)^2 = r^2

before you answer the questions. After you do that, part (a) is just to read off the centre. Then for part (b), you need to know that

r^2 > 0

and hence whatever you end up with on the RHS in terms of

k

, make that > 0 and hence deduce the inequality for

k

Study Forum Helper

Original post by Jeevs090909

Thanks

:smile:

For the other identity question, again, just express the LHS in terms of sines and cosines, get it under the same denominator, then spot the identity

\sin 2\theta = 2 \cos \theta \sin \theta

and use it before coming to a stop at the required result.
For part b, just set the RHS of the identity equal to 1 and observe further what happens why the equality yields no solutions.

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