Question

Can anyone help me?

sin(x + pi/2) = cosx

How do I prove this??

Answer 1

First thing that pops up n my head.

\(\large\color{blue}{ \bf sin(x+90)=cos(x) }\)
\(\large\color{blue}{ \bf sin(x)cos(90)+sin(90)cos(x)=cos(x) }\)

\(\large\color{blue}{ \bf sin(x)~(0)+(1)~cos(x)=cos(x) }\)

....

Answer 2

Just using the sin(a+b) identity

Answer 3

Use the sum formula for sine to simplify the expression. The formula states that sin(A+B)=sinAcosB+cosAsinB.

sin(x)cos(π2)+cos(x)sin(π2)

Take the cosine of π2 to get 0.

sin(x)(0)+cos(x)sin(π2)

Remove the parentheses.

sin(x)⋅0+cos(x)sin(π2)

Multiply sin(x) by 0 to get 0.

(0)+cos(x)sin(π2)

Remove the parentheses.

0+cos(x)sin(π2)

Take the sine of π2 to get 1.

0+cos(x)(1)

Remove the parentheses.

0+cos(x)⋅1

Multiply cos(x) by 1 to get cos(x).

0(cos(x))

Remove the parentheses.

0+cos(x)

Remove the 0 from the polynomial; adding or subtracting 0 does not change the value of the expression.

cos(x)

Answer 4

Oh okay thanks! I guess I just messed up my formula...