Advertisements
Advertisements
प्रश्न
If sin A = `(7)/(25)`, find the value of : `(2"tanA")/"cot A - sin A"`
उत्तर
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
संबंधित प्रश्न
If a right ΔABC , right-angled at B, if tan A=1 then verify that 2sin A . cos A = 1
Evaluate:
cos450 cos300 + sin450 sin300
Evaluate:
`4/(cot^2 30^0) +1/(sin^2 30^0) -2 cos^2 45^0 - sin^2 0^0`
If A = 300 , verify that:
(iii) tan 2A = `(2tanA)/(1-tan^2A)`
`(cos 28°)/(sin 62°)` = ?
If tan x = `1(1)/(3)`, find the value of : 4 sin2x - 3 cos2x + 2
In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ∠ABC.
Given q tan A = p, find the value of:
`("p" sin "A" – "q" cos "A")/("p" sin "A" + "q" cos "A")`.
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
sinB = `sqrt(3)/(2)`
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
cos A = `(7)/(25)`
