All trigonometric equations are identities. true or false?

Question

1Alltrigonometric equations are identities. true or false?

 

My answer: false

 

2

 

cos a/2= +/- √(1-cosa)/2

 

True or false?  False?

 

3

fill in the blank

 

------- cosb=1/2[cos(a+b)+cos(a-b)]

 

a) sina

b) sinb

c) cosa

d) cosb

 

my answer: cosa: c

 

 

correct?  am I correct?  please explain if im not

 

 

Answer 1

1.  You are correct - False, because trig identities are true for ALL angles, whereas trig equations are NOT true for ALL angles.

 

2.  False, correct half angle identity is:
cos a/2 = +/- sqrt((1 + cos a) / 2) 

 

3. You are correct - answer is C (cos a):

 

1/2[cos(a+b) + cos(a-b)] = 

1/2[(cosacosb - sinasinb) + (cosacosb + sinasinb))] =

1/2(2cosacosb) = cosacosb