Maharashtra State BoardHSC Science (General) 11th
Advertisement Remove all ads

If cosecθ + cotθ = 5, then evaluate secθ. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

If cosecθ + cotθ = 5, then evaluate secθ.

Advertisement Remove all ads

Solution

cosecθ + cotθ = 5

∴ `1/sintheta + cos theta/sin theta` = 5

∴ `(1+costheta)/sintheta=5`

∴ 1 + cosθ = 5sinθ

Squaring both the sides, we get

∴ 1 + 2cosθ + cosθ2 = 25sin2θ

∴ 1 + 2cosθ + cos2θ = 25(1 – cos2θ)

∴ 1 + 2cosθ + cos2θ = 25 – 25cos2θ

∴ 26cos2θ + 2cosθ – 24 = 0

∴ 26cos2θ + 26cosθ − 24cosθ – 24 = 0

∴ 26cosθ (cosθ  + 1) – 24(cosθ + 1) = 0

∴ (cosθ + 1) (26cosθ – 24) = 0

∴ cosθ + 1 = 0 or 26cosθ – 24 = 0

∴ cosθ = – 1  or cosθ  = `24/26 = 12/13`

When cosθ = – 1, sinθ = 0

∴ cosecθ and cotθ are not defined.

∴ cosθ ≠ – 1

Hence, cosθ = `12/13`

∴ secθ = `13/12`

Concept: Fundamental Identities
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×