Hi

I have doubts in a problem the iitjee question paper 2012.I have attatched the question image.

1.In line 6 of the solution, why is

1/ 2

2.In line 7 how did we get 5π /6 and why are they adding 2π both the sides?

It sounds like you're diving into some interesting concepts from the IIT JEE question paper! Let's break down the specific lines you're asking about. Although I can't see the image, I can guide you through common scenarios that might relate to your questions about the solution.

Understanding the Fraction in Line 6

When you see a fraction like 1/2 in a solution, it often represents a specific value derived from a formula or a geometric interpretation. For instance, if the problem involves angles or trigonometric functions, 1/2 could represent the sine or cosine of a particular angle. In many cases, this fraction arises from the unit circle, where the coordinates of points correspond to these values. If the context is about finding the area or a specific ratio, that could also explain its presence.

Example of 1/2 in Trigonometry

• If the problem involves a right triangle, the sine of 30 degrees is 1/2.
• In the context of a circle, the radius might be halved, leading to a 1/2 factor in area calculations.

Deciphering Line 7: The Angle and Addition of 2π

Now, regarding the angle of 5π/6, this typically arises from solving trigonometric equations. If the problem involves finding angles that satisfy a certain equation, you might derive 5π/6 from the unit circle, where this angle corresponds to a specific point in the second quadrant. The addition of 2π on both sides is a common technique in trigonometry to account for periodicity. Since trigonometric functions are periodic, adding 2π allows us to find all possible solutions within the range of angles.

Why Add 2π?

• Trigonometric functions repeat every 2π radians.
• This means if you find one solution, there are infinitely many others spaced by 2π.

Putting It All Together

In summary, the fraction 1/2 likely represents a specific trigonometric value or ratio, while the angle of 5π/6 is derived from the unit circle, reflecting a solution to a trigonometric equation. The addition of 2π ensures that all possible angles that satisfy the equation are considered. If you can provide more context or details about the specific problem, I can offer even more tailored insights!