Asked by gaby
Verify that each equation is an identity.
16. 1+tanx/sinx+cosx =secx
ok i have a clue on how to do it. i multiplyed the denominator by sinx-cosx and i also did the top but when i do i get this weird fraction with all these cos and sin and then i get lost...plz help me and explain...
Find a numerical value of one trigonometric function of x.
30. 1+tanx/1+cotx=2
same thing lol..i multiplyed the bottom and top by 1-cotx...then i get stumped...plz explain
16. 1+tanx/sinx+cosx =secx
ok i have a clue on how to do it. i multiplyed the denominator by sinx-cosx and i also did the top but when i do i get this weird fraction with all these cos and sin and then i get lost...plz help me and explain...
Find a numerical value of one trigonometric function of x.
30. 1+tanx/1+cotx=2
same thing lol..i multiplyed the bottom and top by 1-cotx...then i get stumped...plz explain
Answers
Answered by
Reiny
you should use brackets so it looks like
(1+tanx)/(sinx+cosx) =secx
you are on the right track, after multiplying top and bottom by sinx - cosx you get
LS = (1+tanx)(sinx-cosx)/(sin^2 x - cos^2 x)
= (sinx - cosx + sin^2 x/cosx - sinx)/(sin^2x - cos^2x) after expanding
= (sin^2x - cos^2)/cosx ÷ (sin^2x - cos^2x)
= 1/cosx
= secx
= RS
#30 seems to work the same way.
(1+tanx)/(sinx+cosx) =secx
you are on the right track, after multiplying top and bottom by sinx - cosx you get
LS = (1+tanx)(sinx-cosx)/(sin^2 x - cos^2 x)
= (sinx - cosx + sin^2 x/cosx - sinx)/(sin^2x - cos^2x) after expanding
= (sin^2x - cos^2)/cosx ÷ (sin^2x - cos^2x)
= 1/cosx
= secx
= RS
#30 seems to work the same way.
Answered by
gaby
i don't understand the second step..did u turn tan into sin/cos..? because im trying to do it and i cant get it
wat i did for the top is
sinx-cosx+tansinx-cosx
and then sinx-cosx+sin^2/cosx-cosx
can the two cos at the end cancel..thats wats screwing me up i think
wat i did for the top is
sinx-cosx+tansinx-cosx
and then sinx-cosx+sin^2/cosx-cosx
can the two cos at the end cancel..thats wats screwing me up i think
Answered by
Reiny
here is my multiplication for the top
(1+tanx)(sinx-cosx) or
(1+ sinx/cosx)(sinx-cosx) or
sinx - cosx + sin^2x/cosx - sinx/cosx * cosx
= sinx - cosx + sin^2x/cosx - sinx
= -cosx + sin^2x/cosx , now take a common denominator
= (-cos^2x + sin^2x)/cosx
= (sin^2x - cos^2x)/cosx
now you should be able to follow the rest
(1+tanx)(sinx-cosx) or
(1+ sinx/cosx)(sinx-cosx) or
sinx - cosx + sin^2x/cosx - sinx/cosx * cosx
= sinx - cosx + sin^2x/cosx - sinx
= -cosx + sin^2x/cosx , now take a common denominator
= (-cos^2x + sin^2x)/cosx
= (sin^2x - cos^2x)/cosx
now you should be able to follow the rest
Answered by
gaby
yay thnx!
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.