"Is cos x sin x = 1 an..." was answered by our experts

Bradyn Cherry

Answered question

2022-12-21

Is cos x sin x = 1 an identity?

prejudec481

Beginner2022-12-22Added 8 answers

To demonstrate that this is not an identity, simply plug in

0

for

x

\cos (0) \sin (0) = 0 \cdot 1 = 0 \neq 1

In fact, if we use the identity

\sin (2 x) = 2 \sin (x) \cos (x)

we can show that there are no real values for which the questioned equality is true.

\cos (x) \sin (x) = \frac{1}{2} (2 \sin (x) \cos (x)) = \frac{\sin (2 x)}{2}

Because

\sin (2 x) \leq 1

for all

x \in R

(for all real-valued

x

) that means that

\cos (x) \sin (x) \leq \frac{1}{2}

for all real

x

.
The more common trig identity which involves

1

\sin^{2} (x) + \cos^{2} (x) = 1

which is true for all

x

Oliver Garrett

Beginner2022-12-23Added 1 answers

As stated by this

\cos x = \frac{1}{\sin x} = \csc x

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?