Is sin(a)=tan(a)cos(a) ?

The answer to whether sin(a)=tan(a)cos(a) is True

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prove sin(a)=tan(a)cos(a)

prove

sin (a) = tan (a) cos (a)

True

Solution steps

sin (a) = tan (a) cos (a)

Manipulating right side

tan (a) cos (a)

Express with sin, cos

cos (a) tan (a)

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

= cos (a) \frac{sin ( a )}{cos ( a )}

Simplify

cos (a) \frac{sin ( a )}{cos ( a )} : sin (a)

cos (a) \frac{sin ( a )}{cos ( a )}

Multiply fractions:

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

= \frac{sin ( a ) cos ( a )}{cos ( a )}

Cancel the common factor:

cos (a)

= sin (a)

= sin (a)

= sin (a)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{sin ( 2 x )}{cos ( 2 x ) + sin ^{2} ( x )} = 2 tan (x)

tan (θ) sec (θ) (csc (θ) - sin (θ)) = 1

7 cos^{2} (x) + 5 sin^{2} (x) = 6 + cos (2 x)

(1 - sin^{2} (A)) (1 + tan^{2} (A)) = 1