Saturday 29 June 2019

CBSE Class 10 Maths Trigonometry Question: If sinπœƒ + sin²πœƒ = 1, find the value of cos¹²πœƒ + 3cos¹⁰ πœƒ + 3 cos⁸πœƒ + cos⁶πœƒ + 2 cos⁴πœƒ + 2 cos²πœƒ - 2 (#eduvictors)

Class 10 - Trigonometry Identity Based Question

CBSE Class 10 Maths Trigonometry Question: If sinπœƒ + sin²πœƒ = 1, find the value of cos¹²πœƒ + 3cos¹⁰ πœƒ + 3 cos⁸πœƒ + cos⁶πœƒ + 2 cos⁴πœƒ + 2 cos²πœƒ - 2 (#eduvictors)

Question: If sinπœƒ + sin²πœƒ = 1, find the value of 
        cos¹²πœƒ + 3cos¹⁰ πœƒ + 3 cos⁸πœƒ + cos⁶πœƒ + 2 cos⁴πœƒ + 2 cos²πœƒ - 2 


Answer
Given,
sinπœƒ + sin²πœƒ = 1
sinπœƒ + sin²πœƒ = sin²πœƒ + cos²πœƒ

sinπœƒ = cos²πœƒ

= cos¹²πœƒ + 3cos¹⁰ πœƒ + 3 cos⁸πœƒ + cos⁶πœƒ + 2 cos⁴πœƒ + 2 cos²πœƒ - 2

= (cos¹²πœƒ + 3cos¹⁰ πœƒ + 3 cos⁸πœƒ + cos⁶πœƒ) + 2 (cos⁴πœƒ + cos²πœƒ - 1)

= [(cos⁴πœƒ)³ + 3(cos⁴πœƒ)²(cos²πœƒ) + 3(cos⁴πœƒ)(cos²πœƒ)² + (cos²πœƒ)³] + 2(sin²πœƒ + cos²πœƒ - 1)

= (cos⁴πœƒ + cos²πœƒ)³ + 2 (1 - 1)

= (sin²πœƒ + cos²πœƒ)³ + 2(0)

= (1)³ + 0

= 1

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