Is (sec^2(y))= 1/(cos^2(y)) ?

The answer to whether (sec^2(y))= 1/(cos^2(y)) is True

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prove (sec^2(y))= 1/(cos^2(y))

prove

(sec^{2} (y)) = \frac{1}{cos ^{2} ( y )}

True

Solution steps

sec^{2} (y) = \frac{1}{cos ^{2} ( y )}

Manipulating left side

sec^{2} (y)

Express with sin, cos

sec^{2} (y)

Use the basic trigonometric identity:

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

= (\frac{1}{cos ( y )})^{2}

Simplify

(\frac{1}{cos ( y )})^{2} : \frac{1}{cos ^{2} ( y )}

(\frac{1}{cos ( y )})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{cos ^{2} ( y )}

Apply rule

1^{a} = 1

1^{2} = 1

= \frac{1}{cos ^{2} ( y )}

= \frac{1}{cos ^{2} ( y )}

= \frac{1}{cos ^{2} ( y )}

We showed that the two sides could take the same form

\Rightarrow True

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9 sin (7 π - x) = 9 sin (x)

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

Is (sec^2(y))= 1/(cos^2(y)) ?
The answer to whether (sec^2(y))= 1/(cos^2(y)) is True