math problem!?

Question

Sinα = Kosα + x . Find Sin2α in x form.
the answer is Sin2α = 1-x^2. please help me how to do! thank you

Answer 1

sin a = cos a + x
sin a - cos a = x...(1)

sin 2a = 2sin a cos a
= -(-2sin a cos a)
= -(-2sin a cos a + 1 - 1)
= -(-2sin a cos a + sin^2 a + cos^2 a - 1)
= -((sin a - cos a)^2 - 1), substitute (1)
= -(x^2 - 1)
= 1 - x^2

Remember sin^2 a + cos^2 a = 1 is a very important trigs identity.

Answer 2

Sin(2α) = 2Sin(α)Cos(α) and
Sin²(α)+Cos²(α) = 1
so the substitutions should be fairly obvious. You need to 'bang your head' against it a bit more to see what needs to be done. If you don't, you won't learn the material ☺ (Hint: From the equation given
Sin²(α) = Cos²(α) + 2xCos(α) + x²)

It's a lot of work. But, as we say, it develops character ☺


Doug