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 ______.

विकल्प

• 3

• 2

• 1

• 0

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:

Given 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`

= `(sin^2 22^circ + sin^2(90^circ - 22^circ))/(cos^2(90^circ - 68^circ) + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin(90^circ - 63^circ)`

= `(sin^2 22^circ + cos^2 22^circ)/(sin^2 68^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ * cos 63^circ`   ...`[(∵ sin(90^circ - theta) = cos theta),("and" cos(90^circ - theta) = sin theta)]`

= `1/1 + (sin^2 63^circ + cos^2 63^circ)`  ...[∵ sin²θ + cos²θ = 1]

= 1 + 1

= 2