Question

-If 7 sin^2A + 3cos^2A = 4, show that tan A=1/√3​

Answer 1

Step-by-step explanation:

use the trigonometric identity

sin^2A+cos^2A=1

Answer 2

Step-by-step explanation:

7sin^2A+3cos^2A=4

4sin^2A+3sin^2A+3cos^2A=4

4sin^2A+3(sin^2A+cos^2A)=4

4sin^2A+3(1)=4

sin^2A=(4-3)/4

sin^2A=1/4

by taking square root on both sides,

sinA=1/2

cosA=√(1-sin^2A)

cosA=√(1-1/4)

cosA=√3/2

tanA=sinA/cosA

tanA=(1/2)/(√3/2)

tanA=(1/2)*(2/√3)

tanA=1/√3