Question

Can anyone help me with trigonometric identities? (sum and difference identities, evaluating expressions, common angles, Pythagorean identity)

Answer 1

Tell your question.

Answer 2

First, I am supposed to apply the definitions of the sum and difference identities for cosine to 1/2(cos(a-b)-cos(a+b))

Answer 3

And then simplify

Answer 4

Cos(a-b)=cos a cos b -sin a sin b

Answer 5

Right, and then it needs to be cos(a+b)=cosacosb-sinasinb, right?

Answer 6

Similarly, cos(a+b)=cos a cos b - sin a sin b

Answer 7

sorry,

Answer 8

Okay, from there, how do I simplify or combine the two? And what happened to the (1/2)?

Answer 9

cos(a-b)=cosa cosb +sina sinb

Answer 10

I am confused, could you explain?

Answer 11

now, this simplifies to 1/(2sin a sin b)

Answer 12

you understand

Answer 13

1/4sina sinb

Answer 14

Yea! Now, the other side of the equation (which I haven't given you yet) shows sin(a)sin(b), so now I have sin(a)sin(b)=1/(2sin(a)sin(b))

Answer 15

right?

Answer 16

sin(a)sin(b)=1/(2sin(a)sin(b))

Answer 17

this expression is right?

Answer 18

Well originally the equation was sinasinb=1/2(cos(a-b)-cos(a+b)

Then we used the definitions of the sum and difference identities to get
cos(a-b)=cosacosb+sinasinb and cos(a+b)=cosacosb-sinasinb

Then we simplified to 1/(2sinasinb)

So now it should be sinasinb=1/(2sinasinb)

Answer 19

i think it is given in this way:
sina sinb =(1/2)(cos(a-b)-cos(a+b))

Answer 20

Originally, yes

Answer 21

actually cos terms are in numerator

Answer 22

Am i right

Answer 23

cos(a-b)-cos(a+b)=2sin a sin b
(1/2)*2 sin a sin b
=sin a sin b

Answer 24

I think you get your answer.

Answer 25

Thank you @subha