If ( sin(x) = a ) and ( cos(x) = b ), express the expression ( 2sin(x)cos(x) - 2a^2 + 2b^2 ) in its simplest form.

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Accepted Answer

Step:1 ：Step 1: Use the trigonometric identity ( sin(2x) = 2sin(x)cos(x) ) to simplify the first part of the expression. So the expression becomes ( sin(2x) - 2a^2 + 2b^2 )Step:2 ：Step 2: Group the terms to factor by grouping. The expression now becomes ( sin(2x) + 2(b^2 - a^2) )Step:3 ：Step 3: Use the Pythagorean trigonometric identity ( sin^2(x) + cos^2(x) = 1 ) to replace ( b^2 - a^2 ) with ( 1 - 2a^2 ). The expression now simplifies to ( sin(2x) + 2(1 - 2a^2) )Step:4 ：Step 4: Distribute the 2 in the second part of the expression to get ( sin(2x) + 2 - 4a^2 )

Answer

Step: 1 ：Step 1: Use the trigonometric identity ( sin(2x) = 2sin(x)cos(x) ) to simplify the first part of the expression. So the expression becomes ( sin(2x) - 2a^2 + 2b^2 )Step: 2 ：Step 2: Group the terms to factor by grouping. The expression now becomes ( sin(2x) + 2(b^2 - a^2) )Step: 3 ：Step 3: Use the Pythagorean trigonometric identity ( sin^2(x) + cos^2(x) = 1 ) to replace ( b^2 - a^2 ) with ( 1 - 2a^2 ). The expression now simplifies to ( sin(2x) + 2(1 - 2a^2) )Step: 4 ：Step 4: Distribute the 2 in the second part of the expression to get ( sin(2x) + 2 - 4a^2 )

If $\sin (x) = a$ and $\cos (x) = b$ , express the expression $2 \sin (x) \cos (x) - 2 a^{2} + 2 b^{2}$ in its simplest form.

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Popular Problems

If sin⁡(x)=a and cos⁡(x)=b, express the expression 2sin⁡(x)cos⁡(x)−2a2+2b2 in its simplest form.

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Popular Problems

If $\sin (x) = a$ and $\cos (x) = b$ , express the expression $2 \sin (x) \cos (x) - 2 a^{2} + 2 b^{2}$ in its simplest form.