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Homework Statement
Show that
## {(tan φ+sec φ-1)/(tan φ-sec φ+1)}≡ {(1+sin φ)/cos φ}##[/B]
Homework Equations
The Attempt at a Solution
## (sin φ+1-cos φ)/(sin φ+cos φ-1)##[/B]
How did you get this?chwala said:## (sin φ+1-cos φ)/(sin φ+cos φ-1)##
That is what i did...let me look at my working again...fresh_42 said:To deal with expressions ##a-1## in a denominator, it is often useful to expand the quotient by ##a+1\,.##
still not getting...how can you get ##a-1## in denominator?fresh_42 said:No, you expanded the entire thing by ##\cos \varphi##. Now you can go ahead and write the denominator as ##a-1## and make ##a^2-1## out of it.
not really...how ## cos ψ?##fresh_42 said:No, you expanded the entire thing by ##\cos \varphi##. Now you can go ahead and write the denominator as ##a-1## and make ##a^2-1## out of it.
The basic trigonometry identities include the Pythagorean identities, reciprocal identities, quotient identities, and even-odd identities. These identities are used to simplify and solve trigonometric expressions.
To prove trigonometry identities, you must manipulate the expressions using algebraic techniques and apply the basic trigonometry identities. It is important to remember the fundamental trigonometric ratios and identities to successfully prove the identities.
A trigonometric equation is an equation that involves trigonometric functions and can be solved for a specific value, while a trigonometric identity is an equation that holds true for all values of the variables. In other words, an identity is an equation that is always true, whereas an equation can only be true for certain values.
Trigonometry identities can be used to simplify expressions by replacing complicated expressions with simpler ones. By using the basic identities, you can manipulate the expressions and simplify them to a more manageable form.
Trigonometry identities are important because they allow us to simplify and solve complex trigonometric expressions. They are also crucial for solving real-world problems involving angles and distances, such as in navigation, engineering, and physics.