prove 7sec(y)cos(y)=7

Solution

prove

7 sec (y) cos (y) = 7

True

Solution steps

7 sec (y) cos (y) = 7

Manipulating left side

7 sec (y) cos (y)

Express with sin, cos

7 cos (y) sec (y)

Use the basic trigonometric identity:

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

= 7 cos (y) \frac{1}{cos ( y )}

7 cos (y) \frac{1}{cos ( y )} = 7

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

Multiply fractions:

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

= \frac{1 \cdot 7 cos ( y )}{cos ( y )}

Cancel the common factor:

cos (y)

= 1 \cdot 7

Multiply the numbers:

1 \cdot 7 = 7

= 7

= 7

= 7

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + cos ( 2 t )}{sin ( 2 t ) - cos ( t )} = \frac{2 cos ( t )}{2 sin ( t ) - 1}

(1 + sin (a)) (1 - sin (a)) = \frac{1}{sec ^{2} ( a )}

sec (a) (1 - sin^{2} (a)) = cos (a)

cos (x + y) - cos (x - y) = - 2 sin (x) sin (y)

sec (\frac{π}{2} - u) = csc (u)