Advertisements
Advertisements
प्रश्न
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
उत्तर
ΔBDC is a right-angled triangle.
∴ BC2
= BD2 +DC2
= 32 + 42
= 9 + 16
= 25
⇒ BC = 5cm
ΔABC is a right-angled triangle.
∴ AB2
= AC2 - BC2
= 132 - 52
= 169 - 25
= 144
⇒ AB = 12cm
3 - 2 cos ∠BAC + 3 cot ∠BCD
= `3 - 2 xx "AB"/"AC" + 3 xx "DC"/"BD"`
= `3 - 2 xx (12)/(13) + 3 xx (4)/(3)`
= `3 - (24)/(13) + 4`
= `7 - (24)/(13)`
= `(91 - 24)/(13)`
= `(67)/(13)`.
APPEARS IN
संबंधित प्रश्न
In tan θ = 1, find the value of 5cot2θ + sin2θ - 1.
In the given figure, AD is perpendicular to BC. Find:
`(3)/("sin" x) + (4)/("cos" y) - 4 "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 35 sec θ = 37, find the value of sin θ - sin θ tan θ.
If b tanθ = a, find the values of `(cosθ + sinθ)/(cosθ - sinθ)`.
If cotθ = `sqrt(7)`, show that `("cosec"^2θ -sec^2θ)/("cosec"^2θ + sec^2θ) = (3)/(4)`
If 12cosecθ = 13, find the value of `(sin^2θ - cos^2θ) /(2sinθ cosθ) xx (1)/tan^2θ`.
If 12 cotθ = 13, find the value of `(2sinθ cosθ)/(cos^2θ - sin^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")`.
