Advertisements
Advertisements
Question
If sin A = `(7)/(25)`, find the value of : `(2"tanA")/"cot A - sin A"`
Solution
Consider ΔABC, where ∠B = 90°
⇒ sin A = `"Perpendicular"/"Hypotenuse" = "BC"/"AC" = (7)/(25)`
⇒ cosec A = `(1)/"sin A" = (25)/(7)`
By Pythagoras theorem,
AC2 = AB2 + BC2
⇒ AB2
= AC2 - BC2
= 252 - 72
= 625 - 49
= 576
⇒ AB - 24
Now,
cos A = `"Base"/"Hypotenuse" = "AB"/"AC" = (24)/(25)`
tan A = `"Perpendicular"/"Base" = "BC"/"AB" = (7)/(24)`
⇒ cot A = `(1)/"tan A" = (24)/(7)`
`(2"tan A")/"cot A - sin A"`
= `(2 xx 7/24)/(24 / 7 - 7 /25)`
= `(7/12)/(551/175)`
= `(7)/(12) xx (175)/(551)`
= `(1225)/(6612)`.
APPEARS IN
RELATED QUESTIONS
Given 15 cot A = 8. Find sin A and sec A.
if `sec A = 5/4` verify that `(3 sin A - 4 sin^3 A)/(4 cos^3 A - 3 cos A) = (3 tan A - tan^3 A)/(1- 3 tan^2 A)`
If ∠A and ∠B are acute angles such that tan A= Tan B then prove that ∠A = ∠B
Verify each of the following:
(i)`sin 60^0 cos 30^0-cos 60^0 sin 30^0`
Verify each of the following:
(ii)`cos 60^0 cos 30^0+ sin 60^0 sin30^0`
Given: sin θ = `p/q`.
Find cos θ + sin θ in terms of p and q.
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
cos A = `(7)/(25)`
In the given figure, PQR is a triangle, in which QS ⊥ PR, QS = 3 cm, PS = 4 cm and QR = 12 cm, find the value of: sin P
In an isosceles triangle ABC, AB = BC = 6 cm and ∠B = 90°. Find the values of cos2 C + cosec2 C
If 2 cos θ = `sqrt(3)`, then find all the trigonometric ratios of angle θ
