Can anyone help on this trig identities question

https://imgur.com/a/KRbhFSy

Formatting might be off but its asking to show that :
tanxcosx-sin(x)cos^2(x)= (sinx+cos^3(x))/tanx == tan^2x - tanx -1 = 0

Reply 1

mqb2766

Original post

by sreeeeyas

https://imgur.com/a/KRbhFSy
Formatting might be off but its asking to show that :
tanxcosx-sin(x)cos^2(x)= (sinx+cos^3(x))/tanx == tan^2x - tanx -1 = 0

You might want to express everything in terms of sin and cos and aim for getting the final result in that form. Probably the (slightly) simpler way to go in this case.

Reply 2

mqb2766

Original post

by CurlyNerd

1) multiply by tan(x) ....

As per the sticky at the top of the forum, its best to post a hint or two (not full solutions) and let the OP do as much as possible themselves. Could you pls delete?

Reply 3

CurlyNerd

Original post

by mqb2766

As per the sticky at the top of the forum, its best to post a hint or two (not full solutions) and let the OP do as much as possible themselves. Could you pls delete?

Where is this sticky?

Reply 4

mqb2766

Original post

by CurlyNerd

Where is this sticky?

https://www.thestudentroom.co.uk/showthread.php?t=4919248
Its a the top of the maths forum (f38). Thanks.

Reply 5

sreeeeyas

Original post

by mqb2766

You might want to express everything in terms of sin and cos and aim for getting the final result in that form. Probably the simpler way to go in this case. Otherwise make use of the sec^2 = 1 + tan^2 identity

I’ve done this but I just cannot manage to convert all my terms into tan no matter what.

Reply 6

sreeeeyas

Original post

by CurlyNerd

Where is this sticky?

Hello , would u be able to outline the steps u took again because I cannot find the worked solutions for this anywhere

Reply 7

mqb2766

Original post

by sreeeeyas

I’ve done this but I just cannot manage to convert all my terms into tan no matter what.

If youre converting to sin and cos, you could note that the desired result is basically
sin^2 - sin*cos - cos^2 = 0
can you see a way to get to that? If you take the RHS over youll see you have 4 terms so one must "disappear". Also, at the start you could divide each of the two terms by tan (sin/cos), rather than multiplying through by tan. Overall it shouldnt be more than half a dozen lines.

Upload what youve tried if you still cant get it.