- #1
weirdobomb
- 15
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cosθ + sinθ = √2 cos(θ-∏/4)
what are the steps in between?
what are the steps in between?
Expand cos(θ-/4) means to apply the well-known trig expansion cos (A - B) = (cos A)(cos B) + (sin A)(sin B)weirdobomb said:But how would I get from cosθ + sinθ to √2 cos(θ-∏/4)
I can expand and get the original expression but don't understand the other way around.
Are you saying that you can get fromweirdobomb said:But how would I get from cosθ + sinθ to √2 cos(θ-∏/4)
I can expand and get the original expression but don't understand the other way around.
A trigonometric identity is an equation that is true for all values of the variables involved. It is used to simplify and solve trigonometric equations.
The most commonly used trigonometric identities are the Pythagorean identities (sin^2x + cos^2x = 1), the double angle identities (sin2x = 2sinx cosx), and the sum and difference identities (sin(x+y) = sinx cosy + cosx siny).
Trigonometric identities allow us to simplify complex equations and express them in terms of known trigonometric functions. This makes it easier to solve for unknown variables and find solutions to the equations.
Yes, trigonometric identities can be derived from other identities using algebraic manipulation and properties of trigonometric functions. This is often done to simplify a particular equation or to prove a certain identity.
Practice and repetition are key to remembering and applying trigonometric identities. It also helps to understand the concepts behind the identities and how they are derived. Creating flashcards or mnemonic devices can also aid in memorization.