Answer:
cos²x
Step-by-step explanation:
Using the trigonometric identity
• tanx = [tex]\frac{sinx}{cosx}[/tex], then
[tex]\frac{sinxcosx}{tanx}[/tex]
= [tex]\frac{sinxcosx}{\frac{sinx}{cosx} }[/tex]
= sinxcosx × [tex]\frac{cosx}{sinx}[/tex]
cancel the sinx in the multiplier with the sin x on the denominator
= cos²x
Using the trigonometric identity Sin x cos x/ tan x. The trigonometric function will be cos²x.
Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right-angled(not of 90 degrees).
The slanted side is called the hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.
Using the trigonometric identity
tan x = [tex]\dfrac{sin x}{cos x}[/tex],
then
[tex]\dfrac{sin x\times cos x}{tan x}\\\\\dfrac{sin x\times cos x}{sinx/cos x}\\\\= sinxcosx \times \dfrac{cos x}{sin x}\\\\= cos^2x[/tex]
The trigonometric function will be cos²x.
Learn more about trigonometric ratios here:
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