SOLUTION: Use the Pythagorean identities to write the expression as an integer. (a) 7 sin^2 θ + 7 cos^2 θ (b) 7 sin2(θ/4) + 7 cos2(θ/4)

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Question 1156473: Use the Pythagorean identities to write the expression as an integer.
(a)
7 sin^2 θ + 7 cos^2 θ

(b)
7 sin2(θ/4) + 7 cos2(θ/4)

Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
a) Suppose a right triangle has hypotenuse 1 and one angle that is not the right angle theta. By the definition of sine and cosine, the legs have lengths sin%28theta%29 and cos%28theta%29. By the Pythagorean Theorem, sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1 multiplying both sides by 7 gets 7%2Asin%5E2%28theta%29%2B7%2Acos%5E2%28theta%29=7.
b) Dividing theta by 4 in part a) gets 7%2Asin%5E2%28theta%2F4%29%2B7%2Asin%5E2%28theta%2F4%29=7.