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Question: If A = sin<sup>2</sup>q + cos<sup>4</sup>q then " real values of q...

If A = sin2q + cos4q then " real values of q

A

1 £A£ 2

B

34\frac{3}{4}£ A £ 1

C

1316\frac{13}{16}£ A £ 1

D

34\frac{3}{4}£ A £1316\frac{13}{16}

Answer

34\frac{3}{4}£ A £ 1

Explanation

Solution

A = sin2q + cos4 q

Ž A = sin2q + (cos2q)2 £ 1

Also A = sin2q + cos4q

Ž A = 1 – cos2q + cos4q

Ž A = 1 + (cos⁡2θ−12)2\left( \cos^{2}\theta - \frac{1}{2} \right)^{2}–14\frac{1}{4}

Ž A =34\frac{3}{4}+(cos⁡2θ−12)2\left( \cos^{2}\theta - \frac{1}{2} \right)^{2}³ 34\frac{3}{4} so 34\frac{3}{4}£ A £ 1