Question

MATH HELP PLZ!!!

Drag the tiles to the correct boxes to complete the pairs.
Match the expressions with their solution

Answer 1

a)
`tan (157.5) = (1-cos 315)/(sin315)`

b)

`sin (165) =\sqrt{ (1-cos (330) )/(2)}`

c)

`sin^(2) (157.5) = (1-cos (315) )/(2)`

d)

cos 330° = 1- 2 sin² (165°)

Explanation:

Step(i):-

By using trigonometry formulas

a)

cos2∝ = 2 cos² ∝-1

cos∝ = 2 cos² ∝/2 -1

1+ cos∝ = 2 cos² ∝/2

`cos^(2) ((\alpha )/(2)) = (1+cos\alpha )/(2)`

b)

cos2∝ = 1- 2 sin² ∝

cos∝ = 1- 2 sin² ∝/2

`sin^(2) ((\alpha )/(2)) = (1-cos\alpha )/(2)`

Step(i):-

Given

`tan\alpha = (sin\alpha )/(cos\alpha )`

we know that trigonometry formulas

`sin\alpha = 2sin((\alpha )/(2) )cos((\alpha )/(2) )`

1- cos∝ = 2 sin² ∝/2

Given

`tan((\alpha )/(2) ) = (sin((\alpha )/(2) ))/(cos((\alpha )/(2)) )`

put ∝ = 315

`tan((315)/(2) ) = (sin((315 )/(2) ))/(cos((315 )/(2)) )`

multiply with ' 2 sin (∝/2) both numerator and denominator

`tan ((315)/(2) )= (2sin^(2)((315))/(2) )/(2sin((315)/(2) cos((315)/(2)) )`

Apply formulas

`sin\alpha = 2sin((\alpha )/(2) )cos((\alpha )/(2) )`

1- cos∝ = 2 sin² ∝/2

now we get

`tan (157.5) = (1-cos 315)/(sin315)`

b)

`sin^(2) ((\alpha )/(2)) = (1-cos\alpha )/(2)`

put ∝ = 330° above formula

`sin^(2) ((330 )/(2)) = (1-cos (330) )/(2)`

`sin^(2) (165) = (1-cos (330) )/(2)`

`sin (165) =\sqrt{ (1-cos (330) )/(2)}`

c )

`sin^(2) ((\alpha )/(2)) = (1-cos\alpha )/(2)`

put ∝ = 315° above formula

`sin^(2) ((315 )/(2)) = (1-cos (315) )/(2)`

`sin^(2) (157.5) = (1-cos (315) )/(2)`

d)

cos∝ = 1- 2 sin² ∝/2

put ∝ = 330°

`cos 330 = 1 - 2sin^(2) ((330)/(2) )`

cos 330° = 1- 2 sin² (165°)