Given, f(theta)= 11cos^2 (theta) - 9sin^2 (theta) + [15 sin (theta) . Cos (theta)].

Find the Range of the function give above and express the above function in the form of {a cos(2theta+ alpha) + b},where a,b, alpha are real numbers.

I tried using completing the sqaure method but It was no good. Then I tried adding subtracting terms from the function but reached no where.

Please help.


$$F(x)=11\cos^2 x- 9 \sin^2 x+15 \sin x \cos x=1+10 \cos 2x +(15/2) \sin 2x$$ $$\implies F(x)=1+\frac{25}{2} \sin (2x+\alpha)$$ $$\implies F_{min}=1-\frac{25}{2}, F_{max}=1+\frac{25}{2}$$ Hence the rabge of $F(x)$ is $[-23/2,27/2]$

  • $\begingroup$ Thanks @Dr Zafar Ahmed . I m grateful to you. $\endgroup$ – JAO FELIX Jun 4 '20 at 15:14
  • $\begingroup$ @JAO FELIX you are welcome. $\endgroup$ – Z Ahmed Jun 4 '20 at 15:57

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