Class 10 Exam > Class 10 Questions > Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 ...
Start Learning for Free
Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?
Most Upvoted Answer
Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?
Community Answer
Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?
Solution:
Step 1: Rewrite the given trigonometric expressions in terms of basic trigonometric functions.
sin^2 30 = (sin 30)^2 = (1/2)^2 = 1/4
cos^2 45 = (cos 45)^2 = (1/√2)^2 = 1/2
tan^2 30 = (sin 30/cos 30)^2 = (1/√3)^2 = 1/3
sin^2 90 = (sin 90)^2 = 1
cos^2 90 = (cos 90)^2 = 0
Step 2: Substitute the values obtained in step 1 into the given expression.
sin^2 30 cos^2 45 + 4tan^2 30 + 1/2 sin^2 90 - 2cos^2 90
= (1/4) x (1/2) + 4 x (1/3) + 1/2 - 2(0)
= 1/8 + 4/3 + 1/2
= (3/24) + (32/24) + (12/24)
= 47/24
= 1 23/24
Therefore, the value of the given expression is 1 23/24.
Explanation:
The given expression involves trigonometric functions of angles 30, 45 and 90 degrees. We use the basic trigonometric identities to rewrite the expressions in terms of basic trigonometric functions. Then, we substitute the values obtained in the given expression and simplify it to obtain the final result.
Step 1: Rewrite the given trigonometric expressions in terms of basic trigonometric functions.
sin^2 30 = (sin 30)^2 = (1/2)^2 = 1/4
cos^2 45 = (cos 45)^2 = (1/√2)^2 = 1/2
tan^2 30 = (sin 30/cos 30)^2 = (1/√3)^2 = 1/3
sin^2 90 = (sin 90)^2 = 1
cos^2 90 = (cos 90)^2 = 0
Step 2: Substitute the values obtained in step 1 into the given expression.
sin^2 30 cos^2 45 + 4tan^2 30 + 1/2 sin^2 90 - 2cos^2 90
= (1/4) x (1/2) + 4 x (1/3) + 1/2 - 2(0)
= 1/8 + 4/3 + 1/2
= (3/24) + (32/24) + (12/24)
= 47/24
= 1 23/24
Therefore, the value of the given expression is 1 23/24.
Explanation:
The given expression involves trigonometric functions of angles 30, 45 and 90 degrees. We use the basic trigonometric identities to rewrite the expressions in terms of basic trigonometric functions. Then, we substitute the values obtained in the given expression and simplify it to obtain the final result.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?
Question Description
Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?.
Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?.
Solutions for Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? defined & explained in the simplest way possible. Besides giving the explanation of
Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24?, a detailed solution for Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? has been provided alongside types of Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? theory, EduRev gives you an
ample number of questions to practice Sin^2 30 cos^2 45 4tan^2 30 1/2 sin^2 90 - 2cos^2 90 1/24? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup