First slide

Multiple and sub- multiple Angles

Question

The value of the expression $(2 \sin^{2} 91^{\circ} - 1) (2 \sin^{2} 92^{\circ} - 1) \dots (2 \sin^{2} 180^{\circ} - 1)$ is equal to

Moderate

A

0
B

1
C

2⁹⁰
D

2⁹⁰-90

Solution

$(2 \sin^{2} 91^{\circ} - 1) (2 \sin^{2} 92^{\circ} - 1) \dots (2 \sin^{2} 180^{\circ} - 1)$
In this product there exists a factor $(2 \sin^{2} 135^{\circ} - 1)$ which is equal to zero
Thus, the product of all terms is zero.

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