Advertisements
Advertisements
प्रश्न
If 5 cot θ = 12, find the value of : Cosec θ+ sec θ
उत्तर
Consider the diagram below :
5cot θ = 12
cot θ = `(12)/(5)`
i.e.`"base"/"perpendicular" = (12)/(5)`
Therefore if length of base = 12x, length of perpendicular = 5x
Since
base2 + perpendicular2 = hypotenuse2 ...[ Using Pythagoras Theorem]
(12x)2 + (5x)2 = hypotenuse2
hypotenuse2 = 144x2 + 25x2 = 169x2
∴ hypotenuse = 13x
Now
cosec θ = `"hypotenuse"/"perpendicular" = (13x)/(5x) = (13)/(5)`
sec θ = `"hypotenuse"/"base" = (13x)/(12x) = (13)/(12)`
Therefore
cosec θ+sec θ
= `(13)/(5)+(13)/(12)`
= `(221)/(60)`
= `3(41)/(60)`
APPEARS IN
संबंधित प्रश्न
In ΔPQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.
If 8 tan A = 15, find sin A – cos A.
In right angled triangle ΔABC at B, ∠A = ∠C. Find the values of sin A sin B + cos A cos B
If cos θ = `7/25` find the value of all T-ratios of θ .
In a ΔABC , ∠B = 90° , AB= 24 cm and BC = 7 cm find (i) sin A (ii) cos A (iii) sin C (iv) cos C
In the adjoining figure, ΔABC is right-angled at B and ∠A = 450. If AC = 3`sqrt(2)`cm, find (i) BC, (ii) AB.
cos 40° = sin ______°
In ΔABC, ∠B = 90°. If AB = 12units and BC = 5units, find: sinA
In the given figure, AD is the median on BC from A. If AD = 8 cm and BC = 12 cm, find the value of sin x
In the given figure, AD is the median on BC from A. If AD = 8 cm and BC = 12 cm, find the value of `(1)/("sin"^2 x) - (1)/("tan"^2 x)`
