Trig identifies AS

I have a question to solve

Sin X = 3 Cos X

I know I can use the identity so Tan X = 3 and then two solutions…

However, I have tried to squre both sides to use the identity (sin x)^2 + (cos x)^2 =1

So (Sin X)^2 = 9(Cos X)^2
10(Cos X)^2 = 1

And then end up with 4 solutions. (Only 2 are the right answers)

What is my mistake??

Thanks

Reply 1

mqb2766

21

Original post by jellyfish_3

I have a question to solve

Sin X = 3 Cos X

I know I can use the identity so Tan X = 3 and then two solutions…

However, I have tried to squre both sides to use the identity (sin x)^2 + (cos x)^2 =1

So (Sin X)^2 = 9(Cos X)^2
10(Cos X)^2 = 1

And then end up with 4 solutions. (Only 2 are the right answers)

What is my mistake??

Thanks

Youve introduced the extraneous solutions corresponding to tan(x)=-3 by squaring the equation.

Reply 2

Muttley79

20

Original post by jellyfish_3

I have a question to solve

Sin X = 3 Cos X

I know I can use the identity so Tan X = 3 and then two solutions…

However, I have tried to squre both sides to use the identity (sin x)^2 + (cos x)^2 =1

So (Sin X)^2 = 9(Cos X)^2
10(Cos X)^2 = 1

And then end up with 4 solutions. (Only 2 are the right answers)

What is my mistake??

Thanks

x = 3

If we square we get x^2 = 9 which has two solutions x = 3 and x = -3

Trig identifies AS

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