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secondary 4 | A Maths
3 Answers Below
Anyone can contribute an answer, even non-tutors.
Pls help. Thank you
Date Posted: 4 years ago
Views: 246
k = (1 + sinx) / cosx
1/k = cosx / (1 + sinx)
= cosx / (1 + sinx) × (1 - sinx)/(1 - sinx)
(Rationalising the denominator)
= cosx (1 - sinx) / (1² - sin²x)
( (a - b)(a + b) = a² - b²)
= cosx (1 - sinx) / (cos²x)
(1² = 1, 1 - sin²x = cos²x )
= (1 - sinx) / cosx
(Cancel out common factor cosx)
1/k = cosx / (1 + sinx)
= cosx / (1 + sinx) × (1 - sinx)/(1 - sinx)
(Rationalising the denominator)
= cosx (1 - sinx) / (1² - sin²x)
( (a - b)(a + b) = a² - b²)
= cosx (1 - sinx) / (cos²x)
(1² = 1, 1 - sin²x = cos²x )
= (1 - sinx) / cosx
(Cancel out common factor cosx)
k = (1 + sinx) / cosx ①
1/k = (1 - sinx) / cosx ②
① ÷ ② :
k / (1/k) = (1 + sinx) / cosx ÷ (1 - sinx) / cosx
k² = (1 + sinx)/(1 - sinx)
k²(1 - sinx) = 1 + sinx
k² - k² sinx = 1 + sinx
sinx (1 + k²) = k² - 1
sinx = (k² - 1) / (1 + k²)
1/k = (1 - sinx) / cosx ②
① ÷ ② :
k / (1/k) = (1 + sinx) / cosx ÷ (1 - sinx) / cosx
k² = (1 + sinx)/(1 - sinx)
k²(1 - sinx) = 1 + sinx
k² - k² sinx = 1 + sinx
sinx (1 + k²) = k² - 1
sinx = (k² - 1) / (1 + k²)
k = (1 + sinx) / cosx ①
1/k = (1 - sinx) / cosx ②
From ①, k cosx = 1 + sinx
From ②, cosx / k = 1 - sinx
Add these together,
k cosx + cosx / k = 1 + sinx + 1 - sinx
cosx (k + 1/k) = 2
cos x = 2/(k + 1/k)
= 2 / ((k² + 1)/k)
= 2k/(k² + 1)
1/k = (1 - sinx) / cosx ②
From ①, k cosx = 1 + sinx
From ②, cosx / k = 1 - sinx
Add these together,
k cosx + cosx / k = 1 + sinx + 1 - sinx
cosx (k + 1/k) = 2
cos x = 2/(k + 1/k)
= 2 / ((k² + 1)/k)
= 2k/(k² + 1)
See 3 Answers
done
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i’m a sec 4 student too so this was like a practise to me :) hope you understand my solution !! jiayou :)
Date Posted:
4 years ago
edit: seems like my second part is wrong. sorry if it confused you :/
sinx can be found on its own without using the result from cosx. Divide the first equation by the second.
Jona, you can check out an alternative working in the main comments section
Jona, you can check out an alternative working in the main comments section
done
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this is the answer for your earlier question which I believe was deleted.
this question is more challenging and I had to work from both directions in order to see the link.
this question is more challenging and I had to work from both directions in order to see the link.
Date Posted:
4 years ago
tips for solving proving type of questions
1. work from the side which looks more "complicated".
2. know your trigonometric identities well. need not memorize them as most are given in the formula sheet, but you need to learn when and how to apply them.
3. if there are any composite angles (2θ, 3θ, etc), split them out as much as possible).
4. if there are sec, cosec, cot functions, try to convert to sin, cos functions.
5. if you get stuck, you can try to work from the other side to find the link.
however, for final presentation, you need to present the working continuously from one end to the other end.
1. work from the side which looks more "complicated".
2. know your trigonometric identities well. need not memorize them as most are given in the formula sheet, but you need to learn when and how to apply them.
3. if there are any composite angles (2θ, 3θ, etc), split them out as much as possible).
4. if there are sec, cosec, cot functions, try to convert to sin, cos functions.
5. if you get stuck, you can try to work from the other side to find the link.
however, for final presentation, you need to present the working continuously from one end to the other end.
Thank you very much! Really appreciate it.
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