Advertisement Remove all ads

If sinθ = 3 4 , prove that √ cosec 2 θ − cot 2 θ sec 2 θ − 1 = √ 7 3 - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

If sinθ = `(3)/(4)`, prove that `sqrt(("cosec"^2θ - cot^2θ)/(sec^2θ - 1)) = sqrt(7)/(3)`.

Advertisement Remove all ads

Solution

sinθ = `(3)/(4)`

`"Perpendicular"/"Hypotenuse" = (3)/(4)`
Base
= `sqrt(("Hypotenuse")^2 - ("Perpendicuar")^2`
= `sqrt(16 - 9)`
= `sqrt(7)`

cosecθ = `(4)/(3)`

cotθ = `"Base"/"Perpendicular" = sqrt(7)/(3)`

secθ = `"Hypotenuse"/"Base" = (4)/sqrt(7)`

Tp prove `sqrt(("cosec"^2θ - cot^2θ)/(sec^2θ - 1)) = sqrt(7)/(3)`

`sqrt(("cosec"^2θ - cot^2θ)/(sec^2θ - 1)`

= `sqrt(((4/3)^2 - (sqrt(7)/3)^2)/((4/sqrt(7))^2 - 1)`

= `sqrt((16 /9 - 7/9)/(16/7 - 1)`

= `sqrt(((16 - 7)/9)/((16 - 7)/7)`

= `sqrt((9/9)/(9/7)`

= `sqrt((1)/(9/7)`

= `sqrt(7/9)`

= `sqrt(7)/(3)`.

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

APPEARS IN

Frank Class 9 Maths ICSE
Chapter 26 Trigonometrical Ratios
Exercise 26.1 | Q 38
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×