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salantis [7]
3 years ago
5

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

Mathematics
2 answers:
professor190 [17]3 years ago
7 0
You could use the following identities in verifying the trigonometric expression <span>sinx cosx tanx=1-cos^2x:

</span><span>tanx = sinx/cosx
sin^2x+cos^2x = 1
</span>
When those identities are used, you could now verify the equation.

Hope that helps you.
andre [41]3 years ago
5 0

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.


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