Question

If sin A+sin square A=1, then the value of (cos square A + cos raised to the power 4 A) is

(a) 1
(b)
(c) 2
(d) 3

Answer 1

(a) 1 .

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Answer 2

Answer:

Option (a) 1

Step-by-step explanation:

$\sf \Rightarrow sinA + sin^{2} A = 1$

Step 1 : Transposing sin²A to RHS

$\sf \Rightarrow sinA = 1 - sin^{2} A$

Step 3 : Using Trignometric identity cos² A = 1 - sin² A

$\sf \Rightarrow sinA = cos^{2} A$

Step 4 : Squaring on both sides

$\sf \Rightarrow sin^{2} A =( cos^{2} A)^{2}$

Step 5 : Using Laws of exponents ( a^m )^n = a^( mn)

$\sf \Rightarrow sin^{2} A = cos^{2 \times 2} A$

$\sf \Rightarrow sin^{2} A = cos^{4} A$

Step 6 : Using Trignometric identity sin²A = 1 - cos²A

$\sf \Rightarrow 1 - cos^{2} A = cos^{4} A$

Step 7 : Transposing cos²A to RHS

$\sf \Rightarrow 1 = cos^{4} A + cos^{2} A$

$\sf \Rightarrow cos^{4} A + cos^{2} A = 1$

Hence the value cos^4 A + cos²A is 1.