Question

sin4+cos4=1-2sin^2cos^2​

Answer 1

Answer:

Step-by-step explanation:

\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

•••♪