I Need help Please, Geometry
1. If 2. Fill in the blanks for each conjunction, sin 20 = cos __ , sin 33 = cos __ , sin 45 = cos __
3. find the value of x,
3a. sin(x) = cos 31,
3b. sin 75 = cos(x),
3c. sin(x-4) = cos 50

Step-by-step explanation:

\frac{7}{4}

4

7

Explanation:

______________________

We know the values of

i) cos0° = 1

ii) sin45° = \frac{1}{\sqrt{2}}

2

1

iii) sin30° = \frac{1}{2}

2

1

iv) sin90° = 0

v) cos45° = \frac{1}{\sqrt{2}}

2

1

vi ) cos60° = \frac{1}{2}

2

1

_____________________

Now,

The value of

(cos 0+sin 45+sin 30)(sin 90-cos 45+cos 60)

= \left(1+\frac{1}{\sqrt{2}}+\frac{1}{2}\right)\left(1-\frac{1}{\sqrt{2}}+\frac{1}{2}\right)(1+

2

1

+

2

1

)(1−

2

1

+

2

1

)

= \left(\frac{3}{2}+\frac{1}{\sqrt{2}}\right)\left(\frac{3}{2}-\frac{1}{\sqrt{2}}\right)(

2

3

+

2

1

)(

2

3

−

2

1

)

= \left(\frac{3}{2}\right)^{2}-\left(\frac{1}{\sqrt{2}}\right)^{2}(

2

3

)

2

−(

2

1

)

2

/* By algebraic identity

(a-b)(a+b) = a²-b² */

= \left( \frac{9}{4}-\frac{1}{2}\right)(

4

9

−

2

1

)

= \frac{9-2}{4}

4

9−2

= \frac{7}{4}

4

7

••••

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