Question

The value of the expression `(cos^2 12^circ + 2sin12^circ(sin12^circ + 1))/(4cos^2  39^circ - sin^2 78^circ)` is ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

The value of the expression `(cos^2 12^circ + 2sin12^circ(sin12^circ + 1))/(4cos^2  39^circ - sin^2 78^circ)` is 1.00.

Explanation:

`(cos^2 12^circ + 2sin12^circ(sin12^circ + 1))/(4cos^2  39^circ - sin^2 78^circ)`

`(1 - sin^2 12^circ + 2sin12^circ + 2sin^2 12^circ)/(2(1 + cos78^circ) - (1 - cos78^circ)(1 + cos78^circ))`

= `(sin12^circ + 1)^2/((1 + cos78^circ)(2 - 1 + cos78^circ))` 

= `(1 + sin12^circ)^2/((1 + sin12^circ)(1 + sin12^circ))`  

(∵ sin12° = cos78°) = 1