Question

If sin theta + cos theta = root 3, then prove that tan thetha + cot thetha = 1.​

Answer 1

Step-by-step explanation:

sinA +cosA=√3

squaring both side

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

1 + 2sinAcosA=3

2sinAcosA=2

sinAcosA=1. -------------(1)

now,

tanA+cotA =1

sinA/cosA + cosA/SinA=1

(sin^2A+cos^2A)/sinAcosA=1

1 = SinAcosA -----------(ii)

hence proved