Question

HELP <3 Match the expressions with their solutions.

Answer 1

1 ) sin 165°

2 ) cos 330°

3 ) Tan 157.5°

4 )
`sin^2 157.5`

Explanation:

1 )

Given expression is
`\sqrt{(1-cos330)/(2) }`

We know that
`cos2x=1-2sinx^(2)`

`sinx^(2)=(1-cos2x)/(2)`

`(sinx/2)^2=(1-cosx)/(2)`

So the first expression is sin (330/2)° =sin 165°

2 )

GIven expression is
`1-2sin^2165`

We know that
`cos2x=1-2sinx^(2)`

So the result is cos 330°

3 )

Given expression is
`(1-cos 315)/(sin315)`

We know that
`cos2x=1-2sinx^(2)`

Also we know that sin2x = 2sinxcosx

So The numerator becomes
`2sin^2x/2`. and the denominator becomes as
`2sinx/2cosx/2`

`(2sin^2x/2)/(2sinx/2cosx/2)=tanx/2`

So the result is Tan 157.5°

4 )

Given expression is
`(1-cos 315)/(2)`

We know that
`cos2x=1-2sinx^(2)`

`(sinx/2)^2=(1-cosx)/(2)`

So the result is
`sin^2 157.5`