Advertisements
Advertisements
Question
If cotθ = `(1)/sqrt(3)`, show that `(1 - cos^2θ)/(2 - sin^2θ) = (3)/(5)`
Solution
cotθ = `(1)/sqrt(3)`
⇒ cotθ = `(1)/"tanθ" = (1)/sqrt(3) = "Base"/"Perpendicular"`
Hypotenuse
= `sqrt(("Perpendicular")^2 + ("Base")^2`
= `sqrt((sqrt(3))^2 + 1`
= `sqrt(3 + 1)`
= 2
cosθ = `"Base"/"Hypotenuse" = (1)/(2)`,
sinθ = `"Perpendicular"/"Hypotenuse" = sqrt(3)/(2)`
To show: `(1 - cos^2θ)/(2 - sin^2θ) = (3)/(5)`
`(1 - cos^2θ)/(2 - sin^2θ)`
= `(1 - (cosθ)^2)/(2 - (sinθ)^2)`
= `(1 - 1/4)/(2 - 3/4)`
= `(3/4)/(5/4)`
= `(3)/(5)`.
APPEARS IN
RELATED QUESTIONS
In the given figure, ∠Q = 90°, PS is a median om QR from P, and RT divides PQ in the ratio 1 : 2. Find: `("tan" ∠"PSQ")/("tan"∠"PRQ")`
In the given figure, ∠Q = 90°, PS is a median om QR from P, and RT divides PQ in the ratio 1 : 2. Find: `("tan" ∠"TSQ")/("tan"∠"PRQ")`
In the given figure, AD is perpendicular to BC. Find: 15 tan y
In a right-angled triangle ABC, ∠B = 90°, BD = 3, DC = 4, and AC = 13. A point D is inside the triangle such as ∠BDC = 90°.
Find the values of 2 tan ∠BAC - sin ∠BCD
If 4 sinθ = 3 cosθ, find `(6sinθ - 2cosθ )/(6sinθ + 2cosθ )`
If 5cosθ = 3, find the value of `(4cosθ - sinθ)/(2cosθ + sinθ)`
If 4sinθ = `sqrt(13)`, find the value of `(4sinθ - 3cosθ)/(2sinθ + 6cosθ)`
If 5tanθ = 12, find the value of `(2sinθ - 3cosθ)/(4sinθ - 9cosθ)`.
If cosecθ = `1(9)/(20)`, show that `(1 - sinθ + cosθ)/(1 + sinθ + cosθ) = (3)/(7)`
If 12cosecθ = 13, find the value of `(sin^2θ - cos^2θ) /(2sinθ cosθ) xx (1)/tan^2θ`.
