Answer:
[tex]sin^2x+cos^2x=1[/tex] is used to prove the given equation.
Step-by-step explanation:
We have given an equation:
[tex]sinx\cdot cosx\cdot tanx=1-cos^2x[/tex]
We will consider right hand side first
tan x can be written as:
[tex]tanx=\frac{sinx}{cosx}[/tex]
So, on substituting tan x in the left hand side of the given equation we get:
[tex]sinx\cdot cosx\cdot \frac{sinx}{cosx}[/tex]
Cancel common term from denominator and numerator which is cosx we get
[tex]sin^2x[/tex]
And we have an identity:
[tex]sin^2x+cos^2x=1[/tex]
[tex]\Rightarrow sin^2x=1-cos^2x[/tex]
Hence, right hand side is equal to [tex]sin^2x[/tex].
