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Please help me out with this 4 trigonometrytan problems?
1) tanθ + tanα / cotθ + cotα = tanθ × tanα
2) SinA/2 × Sin7A/2 + Sin3A/2 × Sin11A/2 = Sin2A × Sin5A
3) ( Cos3A + Cos5A ) + ( Cos7A + Cos15A )
Please Solve All Three problems
10 points guarantee
For the third problem
( Cos3A + Cos5A ) + ( Cos7A + Cos15A ) = 4 cos4A × Cos5A × cos6A
1 Answer
- hiiLv 65 years agoFavorite Answer
(tanθ + tanα) / (cotθ + cotα)
= [sinθ/cosθ + sinα/cosα] / [cosθ/sinθ + cosα/sinα]
= [(sinθcosα +cosθsinα)/cosθcosα] / [(sinαcosθ + cosαsinθ)/sinθsinα]
= [sin(θ + α)/cosθcosα] / [sin(α + θ)/sinθsinα]
= sinθsinα / cosθcosα
= tanθ⋅tanα
sin(A/2)⋅sin(7A/2) + sin(3A/2)⋅sin(11A/2)
= sin(7A/2)⋅sin(A/2) + sin(11A/2)⋅sin(3A/2)
= (-1/2)[cos(4A) - cos(3A)] + (-1/2)[cos(7A) - cos(4A)]
= (-1/2)[cos(7A) - cos(3A)]
= (-1/2)(-2)[sin(5A)⋅sin(2A)]
= sin(2A)⋅sin(5A)
(cos3A + cos5A) + (cos7A + cos15A)
= (cos15A + cos3A) + (cos7A + cos5A)
= 2⋅cos9A⋅cos6A + 2⋅cos6A⋅cosA
= 2⋅(cos9A + cosA)⋅cos6A
= 2⋅2⋅cos5A⋅cos4A⋅cos6A
= 4⋅cos4A⋅cos5A⋅cos6A
