Question

Sin11'-sin49'/1-2cos^2 54'30

Answer 1

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Answer 2

I can help you with your trigonometry question.

To solve this problem, you need to use some trigonometric identities and algebraic manipulation. Here are the steps:

1. Rewrite the expression using the double angle formula for cosine: $$1-2\cos^2(54^\circ 30') = 2\sin^2(27^\circ 15')$$ 2. Simplify the expression using the sum and difference formulas for sine: $$\sin(11^\circ)-\sin(49^\circ) = 2\cos(30^\circ)\sin(-19^\circ)$$ 3. Divide both sides by $2\cos(30^\circ)$ and simplify: $$\frac{\sin(11^\circ)-\sin(49^\circ)}{1-2\cos^2(54^\circ 30')} = \frac{\sin(-19^\circ)}{\sin^2(27^\circ 15')}$$ 4. Use the reciprocal identity for sine and the negative angle identity for sine: $$\frac{\sin(11^\circ)-\sin(49^\circ)}{1-2\cos^2(54^\circ 30')} = -\frac{\csc(27^\circ 15')}{\sin(19^\circ)}$$ 5. Use a calculator to find the approximate value of the expression: $$\frac{\sin(11^\circ)-\sin(49^\circ)}{1-2\cos^2(54^\circ 30')} \approx -1.414$$

You can check your answer using a trigonometry calculator or a trigonometric equation calculator. You can also learn more about trigonometry and its functions. I hope this helps. Have a nice day.