Question

The expression `(1+sin22^@sin33^@sin35^@)/(cos^2 22^@+cos^2 33^@+cos^2 35^@)` simplifies to

Answer 1

Correct Answer - 0.5
Let `(A)/(2) = 22^(@), (B)/(2) = 33^(@), (C )/(2) = 35^(@)`
`rArr A +B+C= 180^(@)`
In `DeltaABC, cos^(2) ""(A)/(2) + cos^(2)""(B)/(2) +cos^(2) ""(C )/(2)`
`= 2+ 2 sin ""(A)/(2)* sin""(B)/(2)* sin ""(C )/(2)`
Hence, `(1+ sin 22^(@) sin 33^(@) sin 35^(@))/(cos ^(2) 22^(@) + cos ^(2) 33^(@) + cos ^(2) 35^(@)) = (1)/(2)`