Question

cos(a/2)=+-sqrt((1+cos(a))/2) for all values of a-true or false?

Answer 1

Answer:

true

Step-by-step explanation:

for all values of a,cos a satisfies

cos a=2cos²a/2-1

2cos²a/2=1+cos a

cos²a/2=(1+cos a)/2

cos a/2=±√(1+cos a)/2

depending upon where a lies in a quadrant,a/2 will lie accordingly

for example,if a=135, i.e,

π<a<π/2

dividing by 2

π/2<a/2<π/4. range of a/2