Hello everyone! I want to thank everyone who helps me in advance as I'm seriously struggling with two problems. The first one I think I managed to solve, but I would like to know for certain (I will post all the work I did for it) while the second question has me completely confused. The instructions for the questions is to simply verify the trigonometric identities.
2) cos(g+h)cos(g-h) = cos2(g)-cos2(h)
I decided to manipulate the right side and here is what I did:
LHS (left-hand side) = (cos(g)-cos(h))2
LHS = (cos(g)+cos(h))(cos(g)-cos(h))
LHS = cos(g+h)cos(g-h)
cos(g+h)cos(g-h) = cos(g+h)cos(g-h)
That is my final answer, but I would like to know whether I managed to solve the problem properly or if I made a logical error somewhere.
3) (sin(x)-tan(x))(cos(x)-cot(x)) = (cos(x)-1)(cos(x)-1)
As for this problem, I've tried manipulating both sides (not at the same time), and have gotten stuck. Currently, my work is as follows:
(sin(x)-(sin(x)/cos(x)))(cos(x)-(cos(x)/sin(x))) = RHS (right-hand side)
After this part is where I get confuse. Should I subtract the sin(x) and cos(x) in the numerator? I would end up with this:
(1/cos(x))(1/sin(x)) = RHS
Which will give me this:
(sec(x))(csc(x)) = RHS
And that's as far as I managed to get. Any help is appreciated!
2) cos(g+h)cos(g-h) = cos2(g)-cos2(h)
I decided to manipulate the right side and here is what I did:
LHS (left-hand side) = (cos(g)-cos(h))2
LHS = (cos(g)+cos(h))(cos(g)-cos(h))
LHS = cos(g+h)cos(g-h)
cos(g+h)cos(g-h) = cos(g+h)cos(g-h)
That is my final answer, but I would like to know whether I managed to solve the problem properly or if I made a logical error somewhere.
3) (sin(x)-tan(x))(cos(x)-cot(x)) = (cos(x)-1)(cos(x)-1)
As for this problem, I've tried manipulating both sides (not at the same time), and have gotten stuck. Currently, my work is as follows:
(sin(x)-(sin(x)/cos(x)))(cos(x)-(cos(x)/sin(x))) = RHS (right-hand side)
After this part is where I get confuse. Should I subtract the sin(x) and cos(x) in the numerator? I would end up with this:
(1/cos(x))(1/sin(x)) = RHS
Which will give me this:
(sec(x))(csc(x)) = RHS
And that's as far as I managed to get. Any help is appreciated!