Class 11 Exam  >  Class 11 Questions  >  Prove that cot 333 - cos 567/tan 297 + sin 47... Start Learning for Free
Prove that cot 333 - cos 567/tan 297 + sin 477 =1?
Most Upvoted Answer
Prove that cot 333 - cos 567/tan 297 + sin 477 =1?
Given:
cot 333 - cos 567/tan 297 * sin 477

To prove:
cot 333 - cos 567/tan 297 * sin 477 = 1

Proof:

To simplify the given expression, we will break it down into smaller parts and simplify each part step by step.

Step 1: Simplify cot 333
The cotangent function is the reciprocal of the tangent function.
cot 333 = 1 / tan 333

Step 2: Simplify cos 567
The cosine function is periodic with a period of 360 degrees (or 2π radians). Therefore, cos 567 is equivalent to cos (567 - 360) = cos 207.

Step 3: Simplify tan 297
The tangent function is periodic with a period of 180 degrees (or π radians). Therefore, tan 297 is equivalent to tan (297 - 180) = tan 117.

Step 4: Simplify the expression further
Now, we can substitute the simplified values into the expression:
cot 333 - cos 567/tan 297 * sin 477
= 1/tan 333 - cos 207/tan 117 * sin 477

Step 5: Simplify the remaining trigonometric functions
We can use the trigonometric identities to simplify the expression further:
1/tan 333 = cot 333 (since cot 333 = 1/tan 333)
cos 207/tan 117 = cot 117 * cos 207 (since cot θ = 1/tan θ)
cot 117 * cos 207 * sin 477 = cot 117 * sin 477 * cos 207 (since sin θ * cos φ = sin φ * cos θ)

Step 6: Simplify cot 117 * sin 477 * cos 207
cot 117 is the reciprocal of tan 117, so cot 117 = 1/tan 117
cot 117 * sin 477 * cos 207 = 1/tan 117 * sin 477 * cos 207

Step 7: Use trigonometric identities to simplify further
We can use the identity sin 2θ = 2sin θ * cos θ to simplify the expression:
1/tan 117 * sin 477 * cos 207 = 1/tan 117 * sin (2 * 477) * cos 207
= 1/tan 117 * 2sin 477 * cos 477 * cos 207

Step 8: Simplify the expression once again
Using the identity cos (θ + φ) = cos θ * cos φ - sin θ * sin φ, we can simplify further:
1/tan 117 * 2sin 477 * cos 477 * cos 207 = 1/tan 117 * 2sin 477 * (cos (477 + 207))
= 1/tan 117 * 2sin 477 * (cos 477 * cos 207 - sin 477 * sin 207)

Step 9: Simplify the expression to obtain the desired result
Community Answer
Prove that cot 333 - cos 567/tan 297 + sin 477 =1?
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

Prove that cot 333 - cos 567/tan 297 + sin 477 =1?
Question Description
Prove that cot 333 - cos 567/tan 297 + sin 477 =1? 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 Prove that cot 333 - cos 567/tan 297 + sin 477 =1? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that cot 333 - cos 567/tan 297 + sin 477 =1?.
Solutions for Prove that cot 333 - cos 567/tan 297 + sin 477 =1? 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 Prove that cot 333 - cos 567/tan 297 + sin 477 =1? defined & explained in the simplest way possible. Besides giving the explanation of Prove that cot 333 - cos 567/tan 297 + sin 477 =1?, a detailed solution for Prove that cot 333 - cos 567/tan 297 + sin 477 =1? has been provided alongside types of Prove that cot 333 - cos 567/tan 297 + sin 477 =1? theory, EduRev gives you an ample number of questions to practice Prove that cot 333 - cos 567/tan 297 + sin 477 =1? 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