What are you trying to do, simplify the expression above?UltimateSomni said:
UltimateSomni said:Homework Equations
The Attempt at a Solution
multiplied the left equation by (cos x)/(cos x) and the right fraction by (1+sin x)/(1+sin x)
get ((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x)
and I have no idea where to go from here
Mark44 said:
The only thing you did that makes sense is replacing cos2(x) with 1 - sin2(x). I don't get what you did go go from (1 + sin(x))2 to 1 + sin(x) + 1 - sin(x).UltimateSomni said:
Mark44 said:
UltimateSomni said:
The identities for sine, cosine, and tangent are fundamental relationships that describe the ratios of the sides of a right triangle. These identities are:
- sin^2(x) + cos^2(x) = 1
- tan(x) = sin(x)/cos(x)
- 1 + tan^2(x) = sec^2(x)
- 1 + cot^2(x) = csc^2(x)
These identities are used to solve for missing sides or angles of a right triangle and to simplify trigonometric expressions. They also serve as the basis for many other trigonometric identities and equations.
The reciprocal identities, such as csc(x) = 1/sin(x), are formed by taking the reciprocal of the trigonometric function. The quotient identities, such as tan(x) = sin(x)/cos(x), are formed by dividing one trigonometric function by another.
It can be helpful to memorize the acronym "SOH-CAH-TOA" to remember the three basic trigonometric identities: sin(x) = opposite/hypotenuse, cos(x) = adjacent/hypotenuse, and tan(x) = opposite/adjacent. Additionally, practicing and using these identities often can help with memorization.
Yes, there are many other important identities in trigonometry, such as the double angle identities, half angle identities, and sum and difference identities. These can be derived from the basic identities and are used to solve more complex trigonometric equations and problems.