Is sin^2(x)+cos^2(x)=cos(x)sec(x) ?

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

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prove sin^2(x)+cos^2(x)=cos(x)sec(x)

prove

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

True

Solution steps

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

Manipulating right side

cos (x) sec (x)

Express with sin, cos

cos (x) sec (x)

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

= \frac{1 \cdot cos ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= 1

= 1

= 1

Rewrite using trig identities

1

Use the Pythagorean identity:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

(csc (x) + cot (x)) (sec (x) - 1) = tan (x)

cos (x - \frac{π}{2}) = cos (x) tan (x)

csc (- θ) = - csc (θ)

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

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