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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (x) + sin (x) cos (x) tan (x)

Express with sin, cos

cos^{2} (x) + cos (x) sin (x) tan (x)

Use the basic trigonometric identity:

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

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

Simplify

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

cos^{2} (x) + 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)

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

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

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

sin (y) csc (y) = 1

(cos (θ))^{2} = cos^{2} (θ)

\frac{1 + cos ( x )}{cos ( x )} = sec (x) + 1

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

tan (a) + cot (a) = csc (a) sec (a)

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