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Some Important Points to Remember

  1. While solving a trigonometric equation, squaring the equation at any step should be avoided as far as possible. If squaring is necessary, check the solution for extraneous values.
Illustration
Solve the equation sin x + cos x = 1.
 
Solution
If we square we have (sin x + cos x)2 = 1
 
⇒ 1 + sin 2x = 1 ⇒ sin 2x = 0 ⇒ 2x = nπn ∈ Z
 
⇒ x = nπ/2, n ∈ Z
 
But for n = 2, x = π for which sin π + cos π = –1 which does not satisfy the given equation.
 
  1. Never cancel terms containing unknown terms on the two sides, which are in product. It may cause loss of the genuine solution.
  2. The answer should not contain such values of angles which make any of the terms undefined or infinite.
Illustration
Solve: 108293.png = 1.
Solution
tan(3x – 2x) = tan x = 1
 
∴ x = nπ + (π/4)
 
But this value does not satisfy the given equation as tan 2x = tan (π/2) = ∞ and it reduces to indeterminate form.
 
  1. Domain should not change. If it changes, necessary corrections must be made.
  2. Check that denominator is not zero at any stage while solving equations.




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