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- Use a half-angle formula to find the exact value of the following expression.sin ((5\pi )/(8))a) Which of the following is the half-angle formula for sine?A) sin((\theta )/(2)) = ± \sqrt((1+sin\theta )/(2))B) sin((\theta )/(2)) = ± \sqrt((1-sin\theta )/(2))C) sin((\theta )/(2)) = ± \sqrt((1-cos\theta )/(2))D) sin((\theta )/(2)) = ± \sqrt((1+cos\theta )/(2))b) sin ((5\pi )/(8)) = ____ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)Use a double angle formula to find the exact value of 2cos2(pi/6)-1. Type an exact answer using radicals as needed.Evaluate the following expressions. The answer must be given as a fraction, NO DECIMALS. If the answer involves a square root it should be entered as sqrt . For instance, the square root of 2 should be written as sqrt(2). If tan(θ)=−43tan(θ)=-43 and sin(θ)>0sin(θ)>0, then find (a) sin(θ)= (b) cos(θ)= (c) sec(θ)= (d) csc(θ)= (e) cot(θ)=
- Use a product-to-sum identity to rewrite the expression. cos 35° sin 5° cos 35° sin 5°= ____(Simplify your answer. Do not include the degree symbol in your answer. Use integers or fractions for any numbers in the expression.)Prove the following identity. sin 3θ = 3 sin θ − 4 sin3 θ We begin by writing the left side of the equation as the sine of a sum so that we can use a Sum Formula to expand. We can then use the Double-Angle Formulas to replace any terms with double angles. After expanding out the products, we can use a Pythagorean Identity to write the expression in terms of sines.a) Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles. sin2(3x) cos2(3x) b) Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles. cos4(4x)
- Use the Half-Angle Identities to have an exact value for each of the following (use simplified fractions, no decimals!). Assume all angles are in the first quadrant. (a) cos A = 23/49 cos(A/2) = (b) cos A = 31/81 sin(A/2) = (c) cos A = 48/73 tan(A/2) =a) Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles. 7 cos4(x) b)Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles. 2 sin4(2x) c)Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles. 4 tan2(2x) cos4(2x)Use a product-to-sum formula to convert the following expression to a sum or difference and then simplify if possible. sin 3 π 8 sin π 8 SHOW ON YOUR WORKSHEET. Group of answer choices 2 2 2 4 2