Ahem he's done it right so far. If he multiplies top and bottom by cosA+sinA and simplifies it reduces to a well known identity.
Spoiler
Oh sorry I didn't see it, I'll have a look later I did that while getting changed this morning. But I don't think you should use any identity except the main sin cos tang a + b and cos squared and sin squared. Otherwise its cheating a little
Oh sorry I didn't see it, I'll have a look later I did that while getting changed this morning. But I don't think you should use any identity except the main sin cos tang a + b and cos squared and sin squared. Otherwise its cheating a little
Hmm maybe, I don't know.
It's a well known result though.
We're using identities (they hold true for any value of A), so I think it would be allowed .
I know what you mean but my solution assumes a lot less which I think is better.
In which way are you doing it, i did it in a similar way to you by multiply the top and bottom in the LHS by 1+sin2a, getting rid of square root, but then also it wasn't simple to solve it.
So i get LHS as:
Then i tried to show the expression i got for LHS by using RHS, and succeeded in it. So now by seeing the steps in reverse i was able to know how to do the question by just using the LHS and not making any changes to RHS. But how to do it directly, i don't have any clue of how could i have solved it if i wouldn't have tried using both sides.
In which way are you doing it, i did it in a similar way to you by multiply the top and bottom in the LHS by 1+sin2a, getting rid of square root, but then also it wasn't simple to solve it.
So i get LHS as:
Then i tried to show the expression i got for LHS by using RHS, and succeeded in it. So now by seeing the steps in reverse i was able to know how to do the question by just using the LHS and not making any changes to RHS. But how to do it directly, i don't have any clue of how could i have solved it if i wouldn't have tried using both sides.
After where you are, expand cos2a then divide by cos to make everything tan or sec. Then make equations in tan and take common factor (1 + tan a I think) then its clear. And I only manipulated the LHS to work it out
But we're not making assumptions. Identities serve useful purposes, for example in this case .
Anyway fair enough.
It is an assumption if you don't prove it. In a level maths you can only assume what's in the formula booklet and slight variations (like the ones derived from cos squared + sin squared. It's not right to show an identity is true by using some other identity that isn't given. You may or may not get the marks but it's definitely not proper - I think it's worth the extra effort to do it my way
Sorry for poor formatting throughout. I don't like typing on phones.: p
In which way are you doing it, i did it in a similar way to you by multiply the top and bottom in the LHS by 1+sin2a, getting rid of square root, but then also it wasn't simple to solve it.
So i get LHS as:
Then i tried to show the expression i got for LHS by using RHS, and succeeded in it. So now by seeing the steps in reverse i was able to know how to do the question by just using the LHS and not making any changes to RHS. But how to do it directly, i don't have any clue of how could i have solved it if i wouldn't have tried using both sides.
It is an assumption if you don't prove it. In a level maths you can only assume what's in the formula booklet and slight variations (like the ones derived from cos squared + sin squared. It's not right to show an identity is true by using some other identity that isn't given. You may or may not get the marks but it's definitely not proper - I think it's worth the extra effort to do it my way
Sorry for poor formatting throughout. I don't like typing on phones.: p
Again that's like saying you're assuming sin(A+B)= sinAcosB+cosAsinB (simply because you haven't proved it).
Also it is an identity; so you wouldn't be penalised at all. My way is just a shortcut.
Scroll down you'll see where I got it from. It's not an assumption at all.
No no that's not what I'm saying. It is an assumption, anything is an assumption if you don't prove it. What makes the difference is what you're ALLOWED to assume, and you're allowed to quote the formula booklet without proof.
I got it finally :P All i did was divide everything by cos and from there on, it was easy.
Good That's a good direction to take from there too well done (sorry I told you that you were wrong at the start, I didn't look properly - was in the middle of getting changed for 6th form! )