Please help me to prove this..

Step-by-step explanation:

1 / (sin 10°) − √3 / (cos 10°)

Multiply top and bottom of the first fraction by ½ cos 10°.

½ cos 10° / (½ cos 10° sin 10°) − √3 / (cos 10°)

Multiply top and bottom of the second fraction by ½ sin 10°.

½ cos 10° / (½ cos 10° sin 10°) − ½√3 sin 10° / (½ sin 10° cos 10°)

Combine fractions.

(½ cos 10° − ½√3 sin 10°) / (½ sin 10° cos 10°)

Change ½ to sin 30°, and change ½√3 to cos 30°.

(sin 30° cos 10° − cos 30° sin 10°) / (½ sin 10° cos 10°)

Use angle sum formula.

sin(30° − 10°) / (½ sin 10° cos 10°)

sin 20° / (½ sin 10° cos 10°)

Multiply top and bottom by 4.

4 sin 20° / (2 sin 10° cos 10°)

Use double angle formula.

4 sin 20° / sin 20°

4

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

12

step-by-step explanation: