Trigonometric Equations

Given : sin

%5Ctheta

, cos

%5Ctheta

, tan

%5Ctheta

are in G.P.

%5CRightarrow%20%5C%2C%20%5C%2C%20%5C%2C%20cos%5E2%20%5Ctheta%20%5C%2C%20%3D%20%5C%2C%20sin%5Ctheta%20%5C%2C%20tan%5Ctheta%20%5C%2C%20%5CRightarrow%20%5C%2C%20cos%5E3%20%5Ctheta%20%5C%2C%20%3D%20%5C%2C%20sin%5E2%5Ctheta

%5CRightarrow%20%5C%2C%20%5C%2C%20cos%5E3%20%5Ctheta%20%5C%2C%20%3D1-cos%5E2%20%5Ctheta

%5CRightarrow%20%5C%2C%20%5C%2C%20%5C%2C%20(cos%5E3%5Ctheta%20%5C%2C%20%5C%2C%20%2B%20%5C%2C%20cos%5E2%20%5Ctheta)%20%5C%2C%20%3D%201%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%3Cbr%20%2F%3E%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20...(1)

Cubic both sides, we have

cos%5E9%20%5Ctheta%20%2B%20cos%5E6%20%5Ctheta%20%2B%203%20cos%5E5%20%5Ctheta%20.%20(cos%5E3%20%5Ctheta%2B%20cos%5E2%20%5Ctheta)%20%3D1

%5CRightarrow%20%5C%2C%20%5C%2C%20%5C%2C%20cos%5E9%20%5Ctheta%20%2B%20cos%5E6%20%5Ctheta%20%2B%203cos%5E5%20%5Ctheta%20%3D1

%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C

[Using equation (1)]

%5CRightarrow%20%5C%2C%20%5C%2C%20%5C%2C%20cos%5E9%20%5Ctheta%20%2B%20cos%5E6%20%5Ctheta%20%2B%203cos%5E5%20%5Ctheta%20-%201%3D0

Let

%5Ctheta%20%3D%20sin%5E%7B-1%7D%5Cleft%5Bsin%5Cfrac%7B5%5Cpi%7D%7B3%7D%5Cright%5D

%5CRightarrow%20sin%5C%2C%5Ctheta%20%3D%20sin%5Cfrac%7B5%5Cpi%20%7D%7B3%7D%20%3D%20sin%5Cleft%5B2%5Cpi-%5Cfrac%7B%5Cpi%7D%7B3%7D%5Cright%5D

%5CRightarrow%20sin%5C%2C%5Ctheta%20%3D%20-sin%5Cfrac%7B%5Cpi%20%7D%7B3%7D%20%3D%20sin%20%5Cleft(%5Cfrac%7B-%5Cpi%20%7D%7B3%7D%5Cright)

%5Cleft(%5Cbecause%20%5C%2Csin%5C%2C%20%5Cleft(-%20%5Ctheta%20%5Cright)%3D%20%5C%2C-%20%5C%2Csin%20%5C%2C%5Ctheta%5Cright)

Therefore, principal value of

sin%5E%7B-1%7D

%5Cleft%5Bsin%5Cfrac%7B5%5Cpi%20%7D%7B3%7D%5Cright%5D

%5Cfrac%7B-%5Cpi%20%7D%7B3%7D

, as principal value of

sin%5E%7B-%7D

%5E%7B1%7D%20%5C%2Cx

lies between

%5Cfrac%7B-%5Cpi%20%7D%7B2%7D

and

%5Cfrac%7B%5Cpi%20%7D%7B2%7D.

About Trigonometric Equations - VITEEE

Trigonometric Equations is a vital chapter for VITEEE aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

Frequently Asked Questions

Why focus on Trigonometric Equations PYQs?

Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.

How to best use this analysis?

Review the topic breakdown to see which sub-topics within Trigonometric Equations carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

Chapter Questions
6 MCQs

Official Solution

Official Solution

Official Solution

Official Solution

Official Solution

Official Solution

About Trigonometric Equations - VITEEE

Frequently Asked Questions

Why focus on Trigonometric Equations PYQs?

How to best use this analysis?

Trigonometric Equations

High-Yield Trend

Chapter Questions 6 MCQs

Official Solution

Official Solution

Official Solution

Official Solution

Official Solution

Official Solution

About Trigonometric Equations - VITEEE

Frequently Asked Questions

Why focus on Trigonometric Equations PYQs?

How to best use this analysis?

Chapter Questions
6 MCQs