Maths-
General
Easy

Question

Roots of the equation 2 sin squared space theta plus sin squared space theta equals 2 are

  1. straight pi over 6
  2. straight pi over 4
  3. straight pi over 3
  4. straight pi over 2

The correct answer is: straight pi over 4

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To solve a trigonometric inequation of the type sin x ≥ a where |a| ≤ 1, we take a hill of length 2straight pi  in the sine curve and write the solution within that hill. For the general solution, we add 2nstraight pi. For instance, to solve sin space x greater or equal than negative 1 half, we take the hill open square brackets negative pi over 2 comma fraction numerator 3 pi over denominator 2 end fraction close square brackets over which solution is negative pi over 6 less than X less than fraction numerator 7 pi over denominator 6 end fraction The general solution is 2 straight n pi minus pi over 6 less than straight x less than 2 straight n pi plus fraction numerator 7 pi over denominator 6 end fraction, n is any integer. Again to solve an inequation of the type sin x ≤ a, where |a| ≤ 1, we take a hollow of length 2straight pi in the sine curve. (since on a hill, sinx ≤ a is satisfied over two intervals). Similarly cos x ≥ a or cosx ≤a, |a| ≤ 1 are solved.

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