# If tan(cot θ) = cot(tan θ) then sinθ.cosθ = a.1/π b.π c.1/2π d.2/π π denotes pi.

pramodpandey | College Teacher | (Level 3) Valedictorian

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d.   2/pi

tan(cot(theta))=cot(tan(theta))

tan(cot(theta))=tan(pi/2-tan(theta))

cot(theta)=pi/2-tan(theta)

cot(theta)+tan(theta)=pi/2

cos(theta)/sin(theta)+sin(theta)/cos(theta)=pi/2

(cos^2(theta)+sin^2(theta))/(sin(theta)cos(theta))=pi/2

sin(theta)cos(theta)=2/pi

oldnick | (Level 1) Valedictorian

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Set x  as angle
sen (ctg x)/ cos (ctg x) = cos(tg x)/ sen(tg x)\\ developing: sen (ctg x) sen(tg x) = cos(tg x) cos(ctg x) \\cos(tg x)cos(ctg x) - sen(tg x)sen(ctg x) = 0 \\This is the formula for the cosine addition of angles, where the angles are tg x and ctg x \\cos(tg x + cotg x)=0 \\         cos( sen x /cos x + cos x /sen x) = 0 \\                                       now: cosine is zero for x= pigrego/2 or x = 3/2 pigreco Therefore:\\ cos( 1 /senx cosx ) =0 \\1/senx cosx = pigreco /2 \\                1/senx cosx = 3/2 pigreco\\ senx cosx = 2/pigreco\\                         senx cosx = 2/3 pigreco\\ We can also write: sen 2x = 4/pigreco and sen 2x = 4/3 pigreco

oldnick | (Level 1) Valedictorian

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xangle sen (ctg x)/ cos (ctg x) = cos(tg x)/ sen(tg x) developing: sen (ctg x) sen(tg x) = cos(tg x) cos(ctg x) cos(tg x)cos(ctg x) - sen(tg x)sen(ctg x) = 0 This is the formula for the cosine addition of angles, where the angles are tg x and ctg x cos(tg x + cotg x)=0 cos( sen x /cos x + cos x /sen x) = 0 now: cosine is zero for x= pigrego/2 or x = 3/2 pigreco Therefore: cos( 1 /senx cosx ) =0 1/senx cosx = pigreco /2 1/senx cosx = 3/2 pigreco senx cosx = 2/pigreco senx cosx = 2/3 pigreco We can also write: sen 2x = 4/pigreco and sen 2x = 4/3 pigreco