Is cos^2(x)=1-sin(x)*cos(x)*tan(x) ?

The answer to whether cos^2(x)=1-sin(x)*cos(x)*tan(x) is True

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prove cos^2(x)=1-sin(x)cos(x)tan(x)

prove

cos^{2} (x) = 1 - sin (x) \cdot cos (x) \cdot tan (x)

True

Solution steps

cos^{2} (x) = 1 - sin (x) cos (x) tan (x)

Manipulating right side

1 - sin (x) cos (x) tan (x)

Express with sin, cos

1 - cos (x) sin (x) tan (x)

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

= 1 - cos (x) sin (x) \frac{sin ( x )}{cos ( x )}

Simplify

1 - cos (x) sin (x) \frac{sin ( x )}{cos ( x )} : 1 - sin^{2} (x)

1 - cos (x) sin (x) \frac{sin ( x )}{cos ( x )}

cos (x) sin (x) \frac{sin ( x )}{cos ( x )} = sin^{2} (x)

cos (x) sin (x) \frac{sin ( x )}{cos ( x )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{sin ( x ) cos ( x ) sin ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= sin (x) sin (x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= sin^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= sin^{2} (x)

= 1 - sin^{2} (x)

= 1 - sin^{2} (x)

= 1 - sin^{2} (x)

Rewrite using trig identities

1 - sin^{2} (x)

Use the Pythagorean identity:

1 = cos^{2} (x) + sin^{2} (x)

1 - sin^{2} (x) = cos^{2} (x)

= cos^{2} (x)

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) = \frac{( cos ( 2 x ) - 2 )}{- 4}

cot^{2} (x) \frac{1}{csc ( x )} = csc^{2} (x)

(tan (x)) (1 - cot (x)) = tan (x) - 1

tan^{2} (x) - sin^{2} (x) = tan^{2} (x)

sin (x) ((1 + cot^{2} (x))) = csc (x)

Is cos^2(x)=1-sin(x)*cos(x)*tan(x) ?
The answer to whether cos^2(x)=1-sin(x)*cos(x)*tan(x) is True