Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

1 + sec2x sin2x = sec2x

Question

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation. 

1 + sec2x sin2x = sec2x

nottim · Answer

i guess change the left side?

anonymous · Answer

Can you show me how? I don't understand how to apply the identities.

anonymous · Answer

are those 2's all ² ?

anonymous · Answer

Ops, yeah.

anonymous · Answer

No prob. If you hold down the ALT key and press 0179 on the number pad, you can get ². 0179 gives you ³ as well.

as for this problem, can you rewrite sec²x a different way? What is it defined as? Once you do that you should see that something cancels out.

anonymous · Answer

Is it 1+tan^2x ? I couldnt get the thing to work, I dont have a number pad on my computer :(

anonymous · Answer

Yep, and that's an identity as well. http://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity#Related_identities

anonymous · Answer

I'm still confused :/

anonymous · Answer

You're done with the problem! :) The left side is 1 + tan^2x right? There's an identity that says sec^2 x = 1 + tan^2 x , which is what we have here.

anonymous · Answer

What would cancel out?

anonymous · Answer

What about the 1+ in the front and the sin^2x?

anonymous · Answer

Did you change sec ^2 x to 1 / cos^2x on the left hand side?  sorry, there isn't a cancellation, but it will turn into another function.

anonymous · Answer

I'm still confused, do you mind typing out the steps? I'm still not understanding how to get the answer :(

anonymous · Answer

Sure, but I'm going to have you do some work inbetween :)

Step 1: With these identity problems our first step will always be to break apart trig functions into their definitions.

So for this equation we have:
$$1 + \sec ^{2}x \sin^{2}x = \sec^{2}x$$
In order for this to be an identity we need to get the Left hand side equal to the right hand side. If we change the sec²x on the left hand side into $$\frac{ 1 }{ \cos^{2}x }$$, what does the left hand side then simplify into?

anonymous · Answer

Hmmm, would it be$$1+\frac{ 1 }{ \cos^2x }\sin^2x$$ ?

anonymous · Answer

@exitfreshly Do you know to solve this?

anonymous · Answer

My brain hurts too much to try and do trig substitutions right now. Try backsolving what you think might be the answer, maybe; besides that I can't unfortunately be of much help.