Step 1: Baculoviruses are indeed species-specific and have a narrow host range, making them effective for use in short-spectrum insecticide applications. This is a correct statement.
Step 2: Bacillus thuringiensis (Bt) is a bacterium that produces toxins harmful to certain insects, including butterfly caterpillars. Hence, statement (ii) is also correct.
Step 3: Statement (iii) is incorrect as ladybirds are beneficial in controlling aphids and other pest insects, not mosquitoes.
Step 4: Trichoderma fungi are used in biocontrol, but primarily for controlling plant pathogens, not for treating diseased animals. Therefore, statement (iv) is incorrect.
If the value of \( \cos \alpha \) is \( \frac{\sqrt{3}}{2} \), then \( A + A = I \), where \[ A = \begin{bmatrix} \sin\alpha & -\cos\alpha \\ \cos\alpha & \sin\alpha \end{bmatrix}. \]