If cos A + cos²A = 1, then sin² A + sin⁴ A =
Master Class 10th Maths with NCERT solutions and MCQ-based questions from Chapter 9 Some Applications of Trigonometry. Solve exercise questions short-answer problems and detailed explanations to understand real-life applications of trigonometric concepts like heights and distances. These resources align with the CBSE syllabus ensuring thorough exam preparation. Regular practice will enhance problem-solving skills and boost confidence for board exams. Access step-by-step solutions and revision notes tailored to help students achieve excellent results. Begin your preparation today!
Share
We are given the equation:
cos A + cos²A = 1.
We need to find the value of sin²A + sin⁴A.
Step 1: Express cos²A in terms of cos A
Rearrange the given equation:
cos²A = 1 – cos A.
Step 2: Use the Pythagorean identity
From the Pythagorean identity, we know:
sin²A + cos²A = 1.
Substitute cos²A = 1 – cos A into the identity:
sin²A + (1 – cos A) = 1.
Simplify:
sin²A = cos A.
Step 3: Express sin⁴A in terms of sin²A
Since sin²A = cos A, we can write:
sin⁴A = (sin²A)² = (cos A)² = cos²A.
Step 4: Substitute into sin²A + sin⁴A
Now substitute sin²A = cos A and sin⁴A = cos²A into the expression sin²A + sin⁴A:
sin²A + sin⁴A = cos A + cos²A.
From the given equation, we know:
cos A + cos²A = 1.
Thus:
sin²A + sin⁴A = 1.
This question is from Chapter 8 of the Class 10th NCERT Mathematics book, which deals with the Introduction to Trigonometry. Answer the question according to your understanding of the chapter.
For more please visit here:
https://www.tiwariacademy.in/ncert-solutions/class-10/maths/