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Simplifying an expression again

https://www.quora.com/profile/Bravewarrior/p-152921930
I am stuck on the last two lines of working. I managed to get to the third last line, but am struggling to simplify my answer to what they got in the mark scheme in the end. Any help would be great!
Reply 1
Original post by pigeonwarrior
https://www.quora.com/profile/Bravewarrior/p-152921930
I am stuck on the last two lines of working. I managed to get to the third last line, but am struggling to simplify my answer to what they got in the mark scheme in the end. Any help would be great!
The usual
(a+b)/c = a/c + b/c
and 1/cos = sec.
(edited 9 months ago)
Original post by mqb2766
The usual
(a+b)/c = a/c + b/c
and 1/cos = sec.
For some reason I am still confused. How did they get to e^tanx (sec^3 x +secxtanx)? 😭😭
Reply 3
Original post by pigeonwarrior
For some reason I am still confused. How did they get to e^tanx (sec^3 x +secxtanx)? 😭😭
sec/cos^2 =sec*(1/cos)^2 = sec^3
sin/cos^2 = (sin/cos)*(1/cos) = tan*sec

Note if you did it like the other post so
e^tan / cos = e^tan (cos)^(-1)
then product rule gives
sec^2 e^tan / cos + sin e^tan / cos^2 = sec^3 e^tan + sec * tan e^tan = ...
Slighlty simpler but not a huge amout
(edited 9 months ago)
Original post by mqb2766
sec/cos^2 =sec*(1/cos)^2 = sec^3
sin/cos^2 = (sin/cos)*(1/cos) = tan*sec

Note if you did it like the other post so
e^tan / cos = e^tan (cos)^(-1)
then product rule gives
sec^2 e^tan / cos + sin e^tan / cos^2 = sec^3 e^tan + sec * tan e^tan = ...
Slighlty simpler but not a huge amout
Thank you so so much, I finally get it! 😁

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