Question

The value of the expression `{(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ}` is ______.

Answer 1

The value of the expression `{(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ}` is 2.

Explanation:

Note sin 68° = cos 22° and cos 68° = sin 22°.

So `(sin^2 22° + sin^2 68°)/(cos^2 22° + cos^2 68°)`

= `(sin^2 22° + cos^2 22°)/(cos^2 22° + sin^2 22°)`

= 1

Also sin 27° = cos 63°. 

So sin² 63° + cos 63°·sin 27° 

= sin² 63° + cos² 63° 

= 1

Total = 1 + 1

= 2