Question

100 points .......question no6,7,9 ......​

Answer 1

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7)Let (C) be a unit circle, and M∈(C). Also, we will denote ∠IOM as θ (see the diagram). From the unit circle definition, the coordinates of the point M are (cosθ,sinθ). And so, ¯OCis cosθ and ¯OSis sinθ. Therefore, OM=√¯OC2+ ¯OS 2=√cos2θ+sin2θ

. Since M lies in the unit circle, OM is the radius of that circle, and by definition, this radius is equal to 1. It immediately follows that:

cos2θ+sin2θ=1

8)tan(x y) = (tan x tan y) / (1 tan x tan y)

sin(2x) = 2 sin x cos x

cos(2x) = cos2(x) - sin2(x) = 2 cos2(x) - 1 = 1 - 2 sin2(x)

tan(2x) = 2 tan(x) / (1 - tan2(x))

sin2(x) = 1/2 - 1/2 cos(2x)

cos2(x) = 1/2 + 1/2 cos(2x)

sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 )

cos x - cos y = -2 sin( (x-y)/2 ) sin( (x + y)/2 )

$\boxed{Hope\:This\:Helps}$

Answer 2

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