Question

HELP <3 Match the expressions with their solutions.

Answer 1

Answer:

1 ) sin 165°

2 ) cos 330°

3 ) Tan 157.5°

4 ) $sin^2 157.5$

Step-by-step explanation:

1 )

Given expression is  $\sqrt{\frac{1-cos330}{2} }$

We know that $cos2x=1-2sinx^{2}$

$sinx^{2}=\frac{1-cos2x}{2}$

$(sinx/2)^2=\frac{1-cosx}{2}$

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 $\frac{1-cos 315}{sin315}$

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 $2sinx/2cosx/2$

$\frac{2sin^2x/2}{2sinx/2cosx/2}=tanx/2$

So the result is Tan 157.5°

4 )

Given expression is $\frac{1-cos 315}{2}$

We know that $cos2x=1-2sinx^{2}$

$(sinx/2)^2=\frac{1-cosx}{2}$

So the result is $sin^2 157.5$