Help with a simple trigonometric equation

I have a question from the textbook that says. 4tanx = 5sinx , and the solutions were Sin x = 0 and Cos x = 4/5

I understood how I got cos x = 4/5 , but as I cancel out the sin x, how can it be equal to 0? I do not understand where sin comes into play in the solution for this equation, can anyone please explain?

Reply 1

old_engineer

11

You cannot cancel a function that may can have the value zero, as in doing so you are likely to lose solutions. Instead of cancelling sinx, leave it in place and bring both terms onto the same side of the equation. Then take the factor sinx outside a bracket. Now it should be clear that sinx = 0 gives you a solution that would be thrown away if you had cancelled sinx.

Reply 2

lift140

8

Sin^x + cos^x = 1 always, so the solution given in your book is wrong

Reply 3

mqb2766

21

Original post by lift140

Sin^x + cos^x = 1 always, so the solution given in your book is wrong

Original post by old_engineer

You cannot cancel a function that may can have the value zero, as in doing so you are likely to lose solutions. Instead of cancelling sinx, leave it in place and bring both terms onto the same side of the equation. Then take the factor sinx outside a bracket. Now it should be clear that sinx = 0 gives you a solution that would be thrown away if you had cancelled sinx.

The OP's question and post 2 are fine, you factorize solutions rather than dividing by zero.
The identity (pythagoras)
cos^2(x) + sin^2(x) = 1
has nothing to do with this question.

(edited 5 years ago)

Help with a simple trigonometric equation

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