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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating right side

(tan^{2} (x) + 1) (cos^{2} (x) - 1)

Expand

(- 1 + cos^{2} (x)) (1 + tan^{2} (x)) : - 1 - tan^{2} (x) + cos^{2} (x) + cos^{2} (x) tan^{2} (x)

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

Rewrite using trig identities

= - tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) tan (x) cos^{2} (x) = cos (x)

sin (a) sin (b) = sin (a + b)

2 sin (x) = \frac{( 4 cos ( x ) - 1 )}{tan ( x )}

\frac{( 1 - cos ( 4 x ) + sin ( 4 x ) )}{( 1 + cos ( 4 x ) + sin ( 4 x ) )} = 3 sin (2 x)

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

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