Fundamental Identities
Fundamental identities form the bedrock of mathematical expressions, providing a set of equations that remain true for all values of the variables involved. In various branches of mathematics, these fundamental identities serve as the cornerstone for deriving more complex relationships and solving equations. Whether in trigonometry, algebra, or calculus, understanding and manipulating these foundational equations are essential for building a robust mathematical framework. Mastery of fundamental identities empowers individuals to navigate and solve mathematical problems with confidence, enabling a deeper comprehension of the underlying principles that govern diverse mathematical domains.
Questions
- How do you simplify #(sec x - cos x) / tan x#?
- How do you simplify #(sec^4x-1)/(sec^4x+sec^2x)#?
- How do you prove that tangent is an odd function?
- Sec #theta# -1#-:#sec #theta# =?
- How do you simplify the expression #cos^2A(sec^2A-1)#?
- How do you simplify #cot^2x - cot^2x cos^2x#?
- How do you simplify the expression #sint-sintcos^2t#?
- How do you express #sin^2 theta - sec^2 thetacottheta + tan^2 theta # in terms of #cos theta #?
- How do you simplify #Cos(x+pi/6)-sin(x+pi/6)#?
- How do you prove # cos^4theta-sin^4theta)=cos2theta#?
- How do you simplify the expression #(sec^2t-1)/tant#?
- Let θ be an angle in quadrant II, such that #tan θ = (-sqrt15)# how do you find cos θ and csc θ?
- How do you express cosθ csc θ in terms of tanθ?
- How do you perform multiplication and use the fundamental identities to simplify #(sinx+cosx)^2#?
- How do you prove cos(90°-a) = sin(a)?
- How do you simplify the expression #1-sin^2theta#?
- How do you simplify the expression #(secx-1)(secx+1)#?
- How do you prove # tan^2x(1-sin^2x)=(sin^2x-cos2x+cos^2x)/2 #?
- How do you simplify #cos(x - pi/2)#?
- How do you simplify the expression #tan^2xcsc^2x-tan^2x#?