Question

question 21 (mandatory) (1 point)
which expression is equivalent to ( 1 - 2 sin ^ { 2 } \theta ) ?
a) ( 1 - 2 cos ^ { 2 } \theta )
b) ( sin ^ { 2 } \theta )
c) ( cos ^ { 2 } \theta )
d) ( 2 cos ^ { 2 } \theta - 1 )

Explanation:

Step1: Use the Pythagorean identity

We know that \(\sin^{2}\theta+\cos^{2}\theta = 1\), so \(\sin^{2}\theta=1 - \cos^{2}\theta\).

Step2: Substitute \(\sin^{2}\theta\) in the given expression

Substitute \(\sin^{2}\theta = 1-\cos^{2}\theta\) into \(1 - 2\sin^{2}\theta\).

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Answer:

d) \(2\cos^{2}\theta - 1\)