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1. Can somebody please check if my final answers, methods & steps are correct?

Find the set of values of x for which

2) Solve the equation (give general solution as multiples of pi, in radian:

3) Compute the integral [I used the formula : SinACosB = Sin(A+B) + Sin(A-B) A>B]:

4) Find the general solution of theta:

Thank you so much pals! If you are not able to verify all 4 questions, please feel free to check any one(s) that you can.

Thank you again!

Sid
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1. (Original post by Sidhant Shivram)
...
For first one, the quadratic inequality that you reach has additional constraints. Remember that the inequality sign changes when you multiply with a negative. Also, you evaluated the ranges incorrectly.
2. (Original post by Sidhant Shivram)
1. [FONT=CMR12][SIZE=3]Can somebody please check if my final answers, methods & steps are correct...
I don't think what you've said for the first question (about inequalities) is valid. Indeed, if a<b then ac<bc exactly when c is positive. If it is negative then the sign reverses. Therefore, given you can't just multiply by (n-2) say unless you know what the sign of that is.
Here are some possible strategies:
(i) Consider the cases etc. separately (a bit tedious) or
(ii) Multiply by and solve that. (Still a bit tedious, but less so)
(iii) Assume EQUALITY holds, and then check each of the intervals afterwards.
(iv) Use a graphical calculator, but ONLY if this is allowed; the examiner may not like this.
3. (Original post by lazy_fish)
For first one, the quadratic inequality that you reach has additional constraints. Remember that the inequality sign changes when you multiply with a negative. Also, you evaluated the ranges incorrectly.
(Original post by theOldBean)
I don't think what you've said for the first question (about inequalities) is valid. Indeed, if a<b then ac<bc exactly when c is positive. If it is negative then the sign reverses. Therefore, given you can't just multiply by (n-2) say unless you know what the sign of that is.
Here are some possible strategies:
(i) Consider the cases etc. separately (a bit tedious) or
(ii) Multiply by and solve that. (Still a bit tedious, but less so)
(iii) Assume EQUALITY holds, and then check each of the intervals afterwards.
(iv) Use a graphical calculator, but ONLY if this is allowed; the examiner may not like this.
Oh wait! Sorry! My plan was to multiply LHS & RHS with the square of the denominator (a positive number on both sides) and then proceed as usual. I shall post the edited version now. Thanks for pointing that out.
4. (Original post by lazy_fish)
For first one, the quadratic inequality that you reach has additional constraints. Remember that the inequality sign changes when you multiply with a negative. Also, you evaluated the ranges incorrectly.
(Original post by theOldBean)
I don't think what you've said for the first question (about inequalities) is valid. Indeed, if a<b then ac<bc exactly when c is positive. If it is negative then the sign reverses. Therefore, given you can't just multiply by (n-2) say unless you know what the sign of that is.
Here are some possible strategies:
(i) Consider the cases etc. separately (a bit tedious) or
(ii) Multiply by and solve that. (Still a bit tedious, but less so)
(iii) Assume EQUALITY holds, and then check each of the intervals afterwards.
(iv) Use a graphical calculator, but ONLY if this is allowed; the examiner may not like this.

Better?

Thanks again!

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5. (Original post by Sidhant Shivram)
...
Yup.
6. (Original post by lazy_fish)
Yup.
Thanks!

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7. (Original post by Sidhant Shivram)

Better?

Thanks again!

Sent from my iPhone using Tapatalk
next time dont expand it just factor stuff out and expand the linear stuff inside which will give u the roots straight away. ie take it to one side and facto stuff to make it neater and much much quicker.

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8. (Original post by physicsmaths)
next time dont expand it just factor stuff out and expand the linear stuff inside which will give u the roots straight away. ie take it to one side and facto stuff to make it neater and much much quicker.

Posted from TSR Mobile
Oh yes! I see what you mean...Thanks!

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