更新1:
It's (Cos over 1+sin ) + ( 1+sin over cos ) = 2 over Cos I'm supposed to prove/verify that it does equal that.
Prove (Cos/1+sin)+(1+sin/cos)=2/Cos?
回答 (6)
2013-02-16 5:26 pm
✔ 最佳答案
Prove cos/(1 + sin) + (1 + sin)/cos = 2/cos.LHS
= cos/(1 + sin) + (1 + sin)/cos
= [cos^2 + (1 + sin)^2]/[cos(1 + sin)]
= [cos^2 + 1 + 2sin + sin^2]/[cos(1 + sin)]
= [sin^2 + cos^2 + 1 + 2sin]/[cos(1 + sin)]
= 2[1 + sin]/[cos(1 + sin)]
= 2/cos
= RHS
Thus, the equation is true.
2013-02-16 5:25 pm
2016-08-04 4:20 pm
Tan u + cos u /(1+sin u) = tan u + (cos u /(1+sin u)) * ((1-sin u)/(1-sin u)) = tan u + cos u *(1-sin u)/(1-sin^2 u) = tan u + cos u * (1-sin u)/cos^2 u = tan u + (1-sin u)/cos u = tan u + (1/cos u) - (sin u/cos u) = tan u + sec u - tan u = sec u.
2013-02-16 5:27 pm
cosx/(1+sinx) + (1 + sinx)/(cosx)
=(cosx(cosx) + (1+sinx)^2)/((1+sinx)*cosx) (common denominator)
=cos^2x+1+2sinx+sin^2x)/((1+sinx)*cosx) (multiplied out terms)
=(1 + 1 + 2 sinx)/((1+sinx)(cosx)) (sin^2x + cos^2x = 1)
=2(1+sinx)/((1+sinx)(cosx)) (simplified)
=2/cosx
=(cosx(cosx) + (1+sinx)^2)/((1+sinx)*cosx) (common denominator)
=cos^2x+1+2sinx+sin^2x)/((1+sinx)*cosx) (multiplied out terms)
=(1 + 1 + 2 sinx)/((1+sinx)(cosx)) (sin^2x + cos^2x = 1)
=2(1+sinx)/((1+sinx)(cosx)) (simplified)
=2/cosx
2013-02-16 5:26 pm
cosx/(1 + sinx) + (1 + sinx)/cosx
cos^2x/cosx(1 + sinx) + (1 + sinx)^2/cosx(1 + sinx)
(cos^2x + (1 + sinx)^2)/cosx(1 + sinx)
(cos^2x + 1 + 2sinx + sin^2x)/cosx(1 + sinx)
((cos^2x + sin^2x) + 1 + 2sinx)/cosx(1 + sinx)
recall cos^2x + sin^2x = 1
(1 + 1 + 2sinx)/cosx(1 + sinx)
2(1 + sinx)/cosx(1 + sinx)
2/cosx
Find a common denominator, and it becomes pretty clear from there when you notice both sin^2x and cos^2x are in now in the numerator.
cos^2x/cosx(1 + sinx) + (1 + sinx)^2/cosx(1 + sinx)
(cos^2x + (1 + sinx)^2)/cosx(1 + sinx)
(cos^2x + 1 + 2sinx + sin^2x)/cosx(1 + sinx)
((cos^2x + sin^2x) + 1 + 2sinx)/cosx(1 + sinx)
recall cos^2x + sin^2x = 1
(1 + 1 + 2sinx)/cosx(1 + sinx)
2(1 + sinx)/cosx(1 + sinx)
2/cosx
Find a common denominator, and it becomes pretty clear from there when you notice both sin^2x and cos^2x are in now in the numerator.
2013-02-16 5:23 pm
you need to restate that it really does not make any sense
收錄日期: 2021-05-01 14:41:27
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130216091938AAdSO6E