Advertisements
Advertisements
Question
If 12 cotθ = 13, find the value of `(2sinθ cosθ)/(cos^2θ - sin^2θ)`.
Solution
cot θ = `(13)/(12)`
⇒ `cosθ /sinθ = (13)/(12)`
⇒ `"Base"/"Hypotenuse" xx "Hypotenuse"/"Perpendicular" = (13)/(12)`
⇒ `"Base"/"Perpendicular" = (13)/(12)`
Hypotenuse
= `sqrt(("Perpendicular")^2 + ("Base")^2`
= `sqrt((12)^2 + (13)^2`
= `sqrt(144 + 169)`
= `sqrt(313)`
`(2sinθ cosθ)/(cos^2θ - sin^2θ)`
= `(2 xx 12/sqrt(313) xx 13/sqrt(313))/((13/sqrt(313))^2 - (12/sqrt(313))^2`
= `(312/313)/(169/313 - 144/313)`
= `(312/313)/(25/313)`
= `(312)/(25)`.
APPEARS IN
RELATED QUESTIONS
In tan θ = 1, find the value of 5cot2θ + sin2θ - 1.
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
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 3 - 2 cos ∠BAC + 3 cot ∠BCD
If 4 sinθ = 3 cosθ, find tan2θ + cot2θ
If 8tanA = 15, find sinA - cosA.
If 3cosθ - 4sinθ = 2cosθ + sinθ, find tanθ.
If 12cosecθ = 13, find the value of `(sin^2θ - cos^2θ) /(2sinθ cosθ) xx (1)/tan^2θ`.
If secA = `(5)/(4)`, cerify that `(3sin"A" - 4sin^3"A")/(4cos^3"A" - 3cos"A") = (3tan"A" - tan^3"A")/(1 - 3tan^2"A")`.
If tan θ = `"m"/"n"`, show that `"m sin θ - n cos θ"/"m sinθ + n cos θ" = ("m"^2 - "n"^2)/("m"^2 + "n"^2)`
