Question

Prove
sin ^4 A cosec^2 A + cos^4 A sec^2 A = 1.​

Answer 1

Answer:

See Explanation

Step-by-step explanation:

${ \sin}^{4} A \: { \cosec}^{2} A + { \cos}^{4} A \: { \sec}^{2} A = 1 \\ \\LHS = { \sin}^{4} A \: { \cosec}^{2} A + { \cos}^{4} A \: { \sec}^{2} A \\ \\ = { \sin}^{4} A \times \frac{1}{{ \sin}^{2} A} + { \cos}^{4} A \times \frac{1}{{ \cos}^{2} A} \\ \\ = { \sin}^{2} A + { \cos}^{2} A \\ \\ = 1 \\ \\ = RHS \\ \\ hence \: proved$