Is sin(pi/2)=(sqrt(4))/2 ?

The answer to whether sin(pi/2)=(sqrt(4))/2 is True

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prove sin(pi/2)=(sqrt(4))/2

prove

sin (\frac{π}{2}) = \frac{4}{2}

True

Solution steps

sin (\frac{π}{2}) = \frac{4}{2}

Manipulating left side

sin (\frac{π}{2})

Simplify

= 1

Manipulating right side

\frac{4}{2}

Simplify

\frac{4}{2} : 1

\frac{4}{2}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

sec (\frac{π}{4} + a) sec (\frac{π}{4} - a) = 2 sec (2 a)

sin^{4} (x) = sec^{2} (x) tan^{2} (x) + sec^{2} (x)

(1 + cos (x)) (1 - sec (x)) = - 1

cot^{2} (\frac{v}{2}) = \frac{( sec ( v ) + 1 )}{( sec ( v ) - 1 )}

csc (θ) (1 - cos (θ)) (1 + cos (θ)) = sin (θ)