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If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+cos^6x?
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If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+co...
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If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+co...
Solution:
Step 1:
Using the identity sin^2x = 1 - cos^2x, substitute sin^2x in the given equation:
sinx (1 - cos^2x) = 1
sinx - sinx cos^2x = 1
sinx cos^2x = sinx - 1
Step 2:
Squaring both sides of the equation obtained in step 1:
sin^2x cos^4x = sin^2x - 2sinx + 1
Step 3:
Using the identity sin^2x = 1 - cos^2x, substitute sin^2x in the above equation:
(1 - cos^2x) cos^4x = 1 - 2sinx + sin^2x
cos^4x - cos^6x = 1 - 2sinx + (1 - cos^2x)
cos^4x - cos^6x = 2 - 2sinx - cos^2x
Step 4:
Multiplying both sides of the equation obtained in step 3 by cos^6x:
cos^10x - cos^12x = 2cos^6x - 2sinx cos^6x - cos^8x
Step 5:
Using the identity cos^2x = 1 - sin^2x, substitute cos^2x in the above equation:
cos^10x - cos^12x = 2cos^6x - 2sinx cos^6x - (1 - sin^2x)^4
Step 6:
Substituting sin^2x = 1 - cos^2x in the above equation:
cos^10x - cos^12x = 2cos^6x - 2sinx cos^6x - (1 - (1 - cos^2x))^4
cos^10x - cos^12x = 2cos^6x - 2sinx cos^6x - (cos^2x)^4
cos^10x - cos^12x = 2cos^6x - 2sinx cos^6x - cos^8x
Step 7:
Multiplying both sides of the equation obtained in step 6 by cos^2x:
cos^12x - cos^14x = 2cos^8x - 2sinx cos^8x - cos^10x
Step 8:
Substituting the value of cos^12
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If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+cos^6x?
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If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+cos^6x? 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 If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+cos^6x? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+cos^6x?.
If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+cos^6x? 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 If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+cos^6x? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sinx+sin^2x=1 then with the value of cos^12 x+3cos^10x +3cos ^8x+cos^6x?.
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