Question

prove that : ( sin 4 theta + cos 4 theta )/ 1-2 sin square theta cos square theta = 1

Answer 1

Answer:

$\frac{sin^{4}\theta+cos^{4}\theta}{1-2sin^{2}\theta cos^{2}\theta}=1$

Step-by-step explanation:

$LHS= \frac{sin^{4}\theta+cos^{4}\theta}{1-2sin^{2}\theta cos^{2}\theta}\\=\frac{(sin^{2}\theta)^{2}+(cos^{2}\theta)^{2}}{1-2sin^{2}\theta cos^{2}\theta}\\=\frac{(sin^{2}\theta+cos^{2}\theta)^{2}-2sin^{2}\theta cos^{2}\theta }{1-2sin^{2}\theta cos^{2}\theta}$

/* By algebraic identity:

i )a²+b² = (a+b)²-2ab

By Trigonometric identity:

ii) sin²A+cos²A = 1 */

$= \frac{1-2sin^{2}\theta cos^{2}\theta }{1-sin^{2}\theta cos^{2}\theta }\\=1 \\=RHS$

Therefore,

$\frac{sin^{4}\theta+cos^{4}\theta}{1-2sin^{2}\theta cos^{2}\theta}=1$

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Answer 2

Answer:

Step-by-step explanation: