Math Problem Statement

Let π/2 < x < π be such that cot x = -5/√11. Then (sin(11x/2))(sin(6x) - cos(6x)) + (cos(11x/2))(sin(6x) + cos(6x)) is equal to?

Solution

It seems you've uploaded an image. Let me take a look at it and analyze its content to help with any math-related questions. PIL import Image

Load and display the image to understand its content

image_path = '/mnt/data/1733576755754d3tmxncb.jpg' img = Image.open(image_path) img.show()I have displayed the image, but I cannot directly interpret its content just from viewing it. Let me extract and analyze the mathematical information in it. I will review the content for any equations, numbers, or symbols to assist you. pytesseract

Use OCR to extract text from the image

extracted_text = pytesseract.image_to_string(img) extracted_textThe extracted text from the image is "Q3", which suggests this might be part of a larger question or exercise, likely a third question in a set. If you can provide additional context or clarify the problem in question, I'd be happy to assist further with any mathematical details or calculations.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Trigonometric Identities
Quadrants and Angle Analysis

Formulas

cot x = cos x / sin x
sin^2(x) + cos^2(x) = 1
sin(a ± b) = sin(a)cos(b) ± cos(a)sin(b)
cos(a ± b) = cos(a)cos(b) ∓ sin(a)sin(b)

Theorems

Pythagorean Identity
Trigonometric Angle-Sum and Difference Identities

Suitable Grade Level

Grades 11-12