Class 11 Exam  >  Class 11 Questions  >  Tan alpha = sin theta - cos theta /sin theta ... Start Learning for Free
Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha?
Most Upvoted Answer
Tan alpha = sin theta - cos theta /sin theta cos theta , then find s...
Sin alfa equal to 2(sin theta-cos theta)/sin2 theta
equal sin2 theta equal to cos alfa
Community Answer
Tan alpha = sin theta - cos theta /sin theta cos theta , then find s...
Understanding the Equation
To find sin alpha from the given equation, we start by rewriting the expression for tan alpha:
- tan alpha = (sin theta - cos theta) / (sin theta cos theta)
This implies that:
- tan alpha = (A) / (B) where A = sin theta - cos theta and B = sin theta cos theta.
Using the Identity for Sin Alpha
Now, we know that:
- sin alpha = tan alpha / sqrt(1 + tan^2 alpha)
To find sin alpha, we first need to compute tan^2 alpha:
- tan^2 alpha = [(sin theta - cos theta) / (sin theta cos theta)]^2
This can be simplified as:
- tan^2 alpha = (sin^2 theta - 2sin theta cos theta + cos^2 theta) / (sin^2 theta cos^2 theta)
Since sin^2 theta + cos^2 theta = 1:
- tan^2 alpha = (1 - 2 sin theta cos theta) / (sin^2 theta cos^2 theta)
Finding Sin Alpha
Now, substitute tan alpha and tan^2 alpha in the sin alpha formula:
- sin alpha = [(sin theta - cos theta) / (sin theta cos theta)] / sqrt[1 + (1 - 2 sin theta cos theta) / (sin^2 theta cos^2 theta)]
After simplification, we will get the expression for sin alpha.
Final Expression
Thus, the final expression for sin alpha can be derived as:
- sin alpha = (sin theta - cos theta) / sqrt[(sin^2 theta + cos^2 theta)(sin^2 theta cos^2 theta)]
This ultimately leads to the required value of sin alpha based on the values of sin theta and cos theta.
Conclusion
To summarize, by understanding the relationship between tan alpha and its components, we can effectively derive sin alpha.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
Explore Courses for Class 11 exam

Top Courses for Class 11

Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha?
Question Description
Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha?.
Solutions for Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha? in English & in Hindi are available as part of our courses for Class 11. Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha? defined & explained in the simplest way possible. Besides giving the explanation of Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha?, a detailed solution for Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha? has been provided alongside types of Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha? theory, EduRev gives you an ample number of questions to practice Tan alpha = sin theta - cos theta /sin theta cos theta , then find sin alpha? tests, examples and also practice Class 11 tests.
Explore Courses for Class 11 exam

Top Courses for Class 11

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev