prove 9sec(y)cos(y)=9

Solution

prove

9 sec (y) cos (y) = 9

True

Solution steps

9 sec (y) cos (y) = 9

Manipulating left side

9 sec (y) cos (y)

Express with sin, cos

9 cos (y) sec (y)

Use the basic trigonometric identity:

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

= 9 cos (y) \frac{1}{cos ( y )}

9 cos (y) \frac{1}{cos ( y )} = 9

9 cos (y) \frac{1}{cos ( y )}

Multiply fractions:

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

= \frac{1 \cdot 9 cos ( y )}{cos ( y )}

Cancel the common factor:

cos (y)

= 1 \cdot 9

Multiply the numbers:

1 \cdot 9 = 9

= 9

= 9

= 9

We showed that the two sides could take the same form

\Rightarrow True

- sin (- x) = sin (x)

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

csc (x) + sec (x) = tan (x)

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

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