Thank you Reiny for the last question! :)
If you or anyone else could help me with this other question, I'd really appreciate it!
Use the trigonometric subtraction formula for sine to verify the identity:
sin(pi/2-x)=cosx
Caluculation:
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Reason:
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prnt.sc/jns55q <--- copy and paste link
prove sin(pi/2-x)=cosx , use the sin(A-B) = sinAcosB - cosAsinB expansion
LS = sin(π/2 - x)
= sinπ/2cos(x) - cosπ/2sinx , now recall sinπ/2 = 1, cosπ/2 = 0
= cosx - 0(sinx)
= cosx
= RS , all done
OMLLL! Thank you! Ily. :*
To verify the identity sin(pi/2 - x) = cos(x) using the trigonometric subtraction formula for sine, you can follow these steps:
Calculation:
1. Start with the left-hand side of the identity: sin(pi/2 - x).
2. Apply the trigonometric subtraction formula for sine, which states that sin(A - B) = sin(A)cos(B) - cos(A)sin(B).
3. Substitute A = pi/2 and B = x into the formula.
sin(pi/2 - x) = sin(pi/2)cos(x) - cos(pi/2)sin(x)
4. Determine the values of sin(pi/2) and cos(pi/2).
sin(pi/2) = 1 (since sine of pi/2 is equal to 1)
cos(pi/2) = 0 (since cosine of pi/2 is equal to 0)
5. Simplify the equation further.
sin(pi/2 - x) = 1 * cos(x) - 0 * sin(x)
sin(pi/2 - x) = cos(x)
This confirms that the left-hand side is equal to the right-hand side.
Reason:
The trigonometric subtraction formula for sine is derived from the basic trigonometric identities and the relationships between the sine and cosine functions. By using this formula, you can express the difference of two angles in terms of sine and cosine. In this case, we're using the trigonometric subtraction formula to rewrite sin(pi/2 - x) in a form that involves cos(x). The final step shows that the left-hand side of the identity is indeed equal to the right-hand side, verifying the identity.
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