prove that(1+cosA)(1+cosA)= sin^2A
Answers
Answer:
Simplifying
(1 + -1cosA)(1 + cosA) = sin2A
Multiply (1 + -1cosA) * (1 + cosA)
(1(1 + cosA) + -1cosA * (1 + cosA)) = sin2A
((1 * 1 + cosA * 1) + -1cosA * (1 + cosA)) = sin2A
((1 + 1cosA) + -1cosA * (1 + cosA)) = sin2A
(1 + 1cosA + (1 * -1cosA + cosA * -1cosA)) = sin2A
(1 + 1cosA + (-1cosA + -1c2o2s2A2)) = sin2A
Combine like terms: 1cosA + -1cosA = 0
(1 + 0 + -1c2o2s2A2) = sin2A
(1 + -1c2o2s2A2) = sin2A
Solving
1 + -1c2o2s2A2 = in2sA
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1c2o2s2A2 = -1 + in2sA
Combine like terms: 1 + -1 = 0
0 + -1c2o2s2A2 = -1 + in2sA
-1c2o2s2A2 = -1 + in2sA
Divide each side by '-1o2s2A2'.
c2 = o-2s-2A-2 + -1in2o-2s-1A-1
Simplifying
c2 = o-2s-2A-2 + -1in2o-2s-1A-1
Reorder the terms:
c2 = -1in2o-2s-1A-1 + o-2s-2A-2
Reorder the terms:
c2 + in2o-2s-1A-1 + -1o-2s-2A-2 = -1in2o-2s-1A-1 + in2o-2s-1A-1 + o-2s-2A-2 + -1o-2s-2A-2
Combine like terms: -1in2o-2s-1A-1 + in2o-2s-1A-1 = 0
c2 + in2o-2s-1A-1 + -1o-2s-2A-2 = 0 + o-2s-2A-2 + -1o-2s-2A-2
c2 + in2o-2s-1A-1 + -1o-2s-2A-2 = o-2s-2A-2 + -1o-2s-2A-2
Combine like terms: o-2s-2A-2 + -1o-2s-2A-2 = 0
c2 + in2o-2s-1A-1 + -1o-2s-2A-2 = 0
The solution to this equation
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