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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

1 - sin (x) cos (x) cot (x)

Express with sin, cos

1 - cos (x) cot (x) sin (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

= cos (x) cos (x)

Apply exponent rule:

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

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

= cos^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= cos^{2} (x)

= 1 - cos^{2} (x)

= 1 - cos^{2} (x)

= 1 - cos^{2} (x)

Rewrite using trig identities

1 - cos^{2} (x)

Use the Pythagorean identity:

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

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

= sin^{2} (x)

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sec (A) - tan (A) = \frac{cos ( A )}{1 + sin ( A )}

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

sin^{2} (θ) = \frac{3}{4} sin (θ) - \frac{1}{4} sin (3 θ)

\frac{tan ^{2} ( x )}{sec ( x ) + 1} = sec (x)

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

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