Answer the following questions related to the expression .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Answer the following questions related to the expression

\sin^{2}\theta+\cos^{2}\theta

. (i) Explain, with reason, whether the value of

\sin^{2}\theta+\cos^{2}\theta

depends on the measure of

\theta

. State the constant value, if any. (ii) Simplify the expression

5(\sin^{2}\theta-\cos^{2}\theta)

and express your answer without using any power greater than one. (iii) If

\theta=30^{\circ}

, calculate the numerical value of the expression obtained in part (ii).