The Art and Rules of Value-Putting in Trigonometry
Value-putting is the single most powerful shortcut in SSC advanced mathematics. Instead of proving trigonometric identities using multi-line transformations, substitute standard angles into the expression and the four answer options.
- When the expression contains sin θ and cos θ only: Substitute θ = 0° or θ = 90°.
- When the expression contains tan θ, cot θ, sec θ, cosec θ: Substitute θ = 45° (avoids 1/0 indeterminate forms).
- Golden Rule: Never choose an angle that causes division by zero (e.g., tan 90° or cosec 0°).
Key Strategy Takeaway
Value-putting transforms complex trigonometric proofs into elementary 5th-grade arithmetic.
Core x + 1/x Algebraic Identities
Recognize these instantaneous derivations when x + 1/x = k:
- x² + 1/x² = k² - 2
- x³ + 1/x³ = k³ - 3k
- x⁴ + 1/x⁴ = (k² - 2)² - 2
- x⁵ + 1/x⁵ = (x² + 1/x²)(x³ + 1/x³) - (x + 1/x)
- If x + 1/x = 1, then x³ = -1. If x + 1/x = -1, then x³ = 1. If x + 1/x = 2, then x = 1.
Symmetric Algebraic Polynomials
When an algebraic equation has more variables than equations (e.g., a + b + c = 0), set one variable to zero or assume a = b = c to evaluate options in seconds.