Is cos(x - (pi/2)) equal to cos(x)tan(x)?

In summary, verifying trigonometric identities is the process of proving that two expressions involving trigonometric functions are equivalent. This is important for simplifying and manipulating complex trigonometric expressions and solving more complicated equations. Some common techniques for verifying trigonometric identities include using basic trigonometric identities, algebraic properties, and Pythagorean identities. To determine if a trigonometric identity is true, both sides of the equation must simplify to the same expression. If stuck, one can try different techniques and identities or consult a table or seek help. Being able to verify identities is crucial in fields such as physics, astronomy, and navigation.
  • #1
silversorrow
1
0
cos(x-(pie/2))=cos(x)tan(x)

I have to verify this identity and can't seem to figure it out. cos (x-y)=cos x * cos y + sin x * sin y
well since cos y = 0, it kind of eliminates that side of the equation and I end up with sinx * sin1
Did I go about this all wrong?
 
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  • #2
It is sin(x)*1 not sin 1, because sin(pi/2)=1. So far you have cos(x-pi/2)=sin(x), which is correct. Now write out the right hand side of your original equation and see what you get.
 
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What is the purpose of verifying trigonometric identities?

The purpose of verifying trigonometric identities is to prove that two expressions involving trigonometric functions are equivalent. This is important because it allows us to simplify and manipulate complex trigonometric expressions, and to solve more complicated trigonometric equations.

What are some common techniques used to verify trigonometric identities?

Some common techniques used to verify trigonometric identities include using basic trigonometric identities, manipulating expressions using algebraic properties, and using the Pythagorean identities.

How can I tell if a trigonometric identity is true?

A trigonometric identity is considered true if both sides of the equation simplify to the same expression. This can be done by simplifying each side separately and then comparing them to see if they are equivalent.

What should I do if I am stuck while verifying a trigonometric identity?

If you are stuck while verifying a trigonometric identity, try using different techniques and identities, or breaking the expression down into smaller, simpler parts. You can also consult a trigonometric identity table or ask for help from a teacher or tutor.

Why is it important to be able to verify trigonometric identities?

Being able to verify trigonometric identities is important because it allows us to solve more complex trigonometric equations, simplify expressions, and better understand the relationships between different trigonometric functions. It is also a fundamental skill in many fields of science and engineering, such as physics, astronomy, and navigation.

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