Question

What basic trigonometric identity would you use to verify that sinx cosx tanx=1-cos^2x

Answer 1

You could use the following identities in verifying the trigonometric expression sinx cosx tanx=1-cos^2x:

tanx = sinx/cosx
sin^2x+cos^2x = 1

When those identities are used, you could now verify the equation.

Hope that helps you.

Answer 2

Answer:

$sin^2x+cos^2x=1$ is used to prove the given equation.

Step-by-step explanation:

We have given an equation:

$sinx\cdot cosx\cdot tanx=1-cos^2x$

We will consider right hand side first

tan x can be written as:

$tanx=\frac{sinx}{cosx}$

So, on substituting tan x in the left hand side of the given equation we get:

$sinx\cdot cosx\cdot \frac{sinx}{cosx}$

Cancel common term from denominator and numerator which is cosx we get

$sin^2x$

And we have an identity:

$sin^2x+cos^2x=1$

$\Rightarrow sin^2x=1-cos^2x$

Hence, right hand side is equal to $sin^2x$.