Trignometric Identities Problem

[Markd]

A little confused on how to begin the problem


_1__ - tanx sinx = cosx
cosx

I know you change tanx to sinx/cosx but I can't seem to finish the problem, not sure if it is arithmatic errors or what?

 

[da_willem]

Just simplify both sides, by taking the most logical step... And remember $cos^2 x +sin^2 x=1$

 

[dextercioby]

Write everything uder the same denominator.And the definition of tangent and the sine^{2}+cos^{2} connection.

Daniel.

 

[bross7]

You had the right idea starting with $$tanx = \frac{sinx}{cosx}$$

Are you familiar with the trig identity: $$sin^2 x + cos^2 x = 1$$. In many trig question, you have to multiply/divide out parts of your equation to work out the final solution. Take a look at the question and see if there are any common values that would be worth taking out.

 

[Markd]

Alright so

_1__ - tanx sinx = cosx
cosx
_1__ - sinx sinx = cosx
cosx cosx
_1__ - sinx
cosx cosx

Or is it

cosx-cosxsinx * sinx
` 1```` 1 ```````1

 

[Ryoukomaru]

$$\frac{1}{cos\theta}-\frac{sin^2\theta}{cos\theta}=cos\theta$$
Now find a common denominator and simplify it.

 

[dextercioby]

OMG,okay here goes
$$\frac{1}{\cos x}-\frac{\sin x}{\cos x} \sin x=...$$

Can u take it from here?

Daniel.

 

[p53ud0 dr34m5]

ok, i guess ill provide a little more help:
$$\frac{1}{cos\theta}-tan\theta sin\theta=cos\theta$$

simplify the tan:
$$\frac{1}{cos\theta}-\frac{sin\theta}{cos\theta}sin\theta=cos\theta$$

multiply and subtract, because you have like denominators:
$$\frac{1-sin^2\theta}{cos\theta}=cos\theta$$

now, use the fact that $sin^2\theta + cos^2\theta = 1$ to solve.