The answer to whether sin(a)csc(a)=1 is True

prove sin(a)csc(a)=1

Solution

prove

sin (a) csc (a) = 1

True

Solution steps

sin (a) csc (a) = 1

Manipulating left side

sin (a) csc (a)

csc (a) sin (a) = 1

csc (a) sin (a)

Express with sin, cos

csc (a) sin (a)

Use the basic trigonometric identity:

csc (a) = \frac{1}{sin ( a )}

= \frac{1}{sin ( a )} sin (a)

\frac{1}{sin ( a )} sin (a) = 1

\frac{1}{sin ( a )} sin (a)

Multiply fractions:

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

= \frac{1 sin ( a )}{sin ( a )}

Cancel the common factor:

sin (a)

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

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p ro v e cos (33 0^{\circ}) = 1 - 2 sin^{2} (16 5^{\circ})

p ro v e tan^{4} (x) = sec^{4} (x) - sec^{2} (x)

p ro v e cot (x) = \frac{- cos ^{2} ( x )}{( sin ( x ) + 1 ) ^{2}}

p ro v e (1 - tan^{2} (θ)) = sec^{2} (θ) - 4 tan^{2} (θ)