Question

if sin A + cosec A = 2; find the value of sin2 A + cosec2 A.

Answer 1

Answer:

sin A + cosec A = 2

Squaring this on both sides, we get

sin^2A + cosec^2A + 2 sinA cosecA = 4

sin^2A + cosec^2A = 4 - 2 sinAcosecA

But we know that

cosec A = 1/sinA

so we get sinA cosecA = sinA * 1/sinA = 1

so we get

sin^2A + cosec^2A = 4 -2 = 2

sin^2A + cosec^2A = 2

Answer 2

Step-by-step explanation:

sinA+ cosecA=2

squaring on both sides

(sinA+cosecA)2=2^2

using : (a+b)= a^2+b^2+2*a*b

sin^2A+cosec^2A+2*sinA*cosecA

sin^2A+ cosec^2A= 4-2sinAcosecA

cosecA=1/sinA

sin^2A+cosec^2A=4-2

sin^2+cosec^2A=2 (ans)

hope it helps you