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

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.

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flightbath flightbath · Answer 2 · 2018-12-26T05:11:37-05:00

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 \(sin^2x\).