Prove the half-angle identity sin A/2 = +√((1 - cos A)/2) Square both sides: Multiply both sides by 2, and write A = 2( 2 using a )=( Then, the right-hand side of the last equation can be written as ²0 ) + ²0 the last expression simplifies to 2 -angle identity for cosine. By applying ) to get x = sin ) X completing the proof. Use the notation sin²x, cos²x, etc. for powers of tria functions. A)/ 20 ) )

Q: 1-cos?x Simplify: sin²x

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Q: х х sin sin2 cos 2 dx. 2

A: Given integral : I=∫0π2  sin2x2  cos2x2   dx

Q: п — 1 - sin" xdx sin"-2 xdx. n

A:

Q: Express y in terms of x if the inverse sine of x is equal to the inverse tan of y.

A: Given sin-1x=tan-1y.  Assume θ=sin-1x so sinθ=x. Therefore using identity sin2θ+cos2θ=1:…

Q: sin x sin y =

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Q: sin 4x dx 1+cos2x

A: To evaluate the integral: ∫sin4x1+cosx22xdx Solution: Let substitute t=1+cos22x Differentiating both…

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A: Given trigonometric expression is cos2π3-sin2π3.

Q: b. What is the range of y = sin-12x? %3D

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Q: Simplify [2(cos 10 degree + i sin 10 degree )]5 . Give your answer in trigonometric form.

A: We have to simplify: 2cos 10°+i sin 10°5 We know from de Moivre's theorem, cos x+i sin xn=cos nx+i…

Q: Show sin 3A = 3 sin A cos²A - sin A.

A: Explanation: Given that: sin3A=3sinAcos2A-sinA Concept: sin3A=3sinA-4sin3A sin2A+cos2A=1

Q: Show that sin 2x Þ 2 sin x by substituting 30 degree for x and then simplifying both sides.

A: To prove: sin2x≠2sinx For x=30°

Q: 5T Evaluate the expression sin Cos 3.

A: