Understanding and Solving Trigonometry Equations: Tips and Tricks

[Dragonetti]

Homework Statement

Hi,
This isn't a homework question, I am having a bit of trouble with some Trig equations. If you are worried that you are answering a homework question please give me the solution to a similar question.

Homework Equations

When we have a trig equation like sec²X + tan²X = 6.

I know that sec is equal to 1/cos, and tan is equal to sin/cos, but what do I do with the square? Do I square all the terms or just the denominator?

The Attempt at a Solution

I have tried many times, to many to list here!

Thanks for your help
Dominic

 

[jhae2.718]

Hint: is there a Pythagorean identity that relates secant and tangent?

 

[tiny-tim]

Hi Dominic!

When we have a trig equation like sec²X + tan²X = 6.

I know that sec is equal to 1/cos, and tan is equal to sin/cos, but what do I do with the square? Do I square all the terms or just the denominator?

The whole thing …

tan²x = sin²x/cos²x

(and you can also use one of the standard https://www.physicsforums.com/library.php?do=view_item&itemid=18" …

sec²x = tan²x + 1, same as 1/cos²x = sin²x/cos²x + cos²x/cos²x )​