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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Which sum or difference identity would you use to verify that sin (90° + q) = cos q?
cos (a - b) = cos a cos b + sin a sin b
sin (a + b) = sin a cos b + cos a sin b
sin (a - b) = sin a cos b - cos a sin b
cos (a + b) = cos a cos b - sin a sin b
Solution:
We have to verify which sum or difference identity will prove sin (90° + q) = cos q
Using the formula,
Sin(A + B) = sinA cosB + cosA sinB
Substituting in the above formula, we get
So, sin(90° + q) = sin 90°cos q + cos 90° Sin q
The value of sin 90° = 1
The value of cos 90° = 0
So, sin(90° + q) = (1) cos q + (0) sin q
sin(90° + q) = cos q + 0
sin(90° + q) = cos q
Therefore, the identity used to verify sin(90° + q) = cos q is sin (a + b) = sin a cos b + cos a sin b.
Which sum or difference identity would you use to verify that sin (90° + q) = cos q?
Summary:
The identity used to verify sin(90° + q) = cos q is sin (a + b) = sin a cos b + cos a sin b.
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