Verify the Identity sin(A+B)=cos(pi/2-(A+B))

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Trigonometry

$\sin (A + B) = \cos (\frac{π}{2} - (A + B))$

Start on the right side.

$\cos (\frac{π}{2} - (A + B))$

Apply the difference of angles identity $\cos (x - y) = \cos (x) \cos (y) + \sin (x) \sin (y)$ .

$\cos (\frac{π}{2}) \cos (A + B) + \sin (\frac{π}{2}) \sin (A + B)$

Simplify the expression.

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Simplify each term.

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The exact value of $\cos (\frac{π}{2})$ is $0$ .

$0 \cos (A + B) + \sin (\frac{π}{2}) \sin (A + B)$

Multiply $0$ by $\cos (A + B)$ .

$0 + \sin (\frac{π}{2}) \sin (A + B)$

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$0 + 1 \sin (A + B)$

Multiply $\sin (A + B)$ by $1$ .

$0 + \sin (A + B)$

Add $0$ and $\sin (A + B)$ .

$\sin (A + B)$

Because the two sides have been shown to be equivalent, the equation is an identity.

$\sin (A + B) = \cos (\frac{π}{2} - (A + B))$ is an identity

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Name

Name	one hundred fifty-five million six hundred fifty-two thousand one hundred seventy-four

Interesting facts

155652174 has 8 divisors, whose sum is 234082728
The reverse of 155652174 is 471256551
Previous prime number is 387

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 36
Digital Root 9

Name

Name	one billion two hundred fifty-seven million four hundred ninety-five thousand seven hundred thirty

Interesting facts

1257495730 has 8 divisors, whose sum is 2263492332
The reverse of 1257495730 is 0375947521
Previous prime number is 5

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 43
Digital Root 7

Name

Name	one billion nine hundred fifty-four million two hundred sixty-one thousand six hundred sixty-six

Interesting facts

1954261666 has 16 divisors, whose sum is 3359825856
The reverse of 1954261666 is 6661624591
Previous prime number is 347

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 46
Digital Root 1

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