Please solve q 3?
2 Answers
The answer is 10, or D.
Explanation:
You can see that
#sin^2(5˚) + sin^2(85˚)# can be written as
#sin^2alpha + sin^2(90 - alpha)# . This can be simplified as follows:
#sin^2alpha + (sin90cosalpha - cos90sinalpha)^2 = sin^2alpha + cos^2alpha = 1#
Now we examine our series:
#sin^2(5˚) + sin^2(10˚) + sin^2(15˚) + ... + sin^2(75˚) + sin^2(80˚) + sin(85˚) + sin^2(90˚)#
Each term cancels out (
So we now make a table:
#0, 90#
#5, 85#
#10, 80#
#15, 75#
#20, 70#
#25, 65#
#30, 60#
#35, 55#
#40, 50#
#45, 45#
Each of these pairs have a value of
Thus the sum is
Hopefully this helps!
Explanation:
we need to remember that
so
etc.
.