Question:
A vertical lamp-post 6 m height stands at a distance of 2 m from a wall, 4 m high. A 1 -5 m tall man starts to walk away from the wall on the other side of the wall in line with the lamp-post. The maximum distance to which the man can walk, remains in the shadow is
A vertical lamp-post 6 m height stands at a distance of 2 m from a wall, 4 m high. A 1 -5 m tall man starts to walk away from the wall on the other side of the wall in line with the lamp-post. The maximum distance to which the man can walk, remains in the shadow is
Updated On: Jul 6, 2022
- $\frac {5} {2} m$
- $\frac {3} {2} m$
- 4 m
- none of these.
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The Correct Option is A
Solution and Explanation
BD is the reqd. distance
From similar triangles
$\frac{6}{4} = \frac{QR}{BR} \, i.e., \, \frac{3}{2} = \frac{2 + BR}{BR} \Rightarrow BR = 4$
$\frac{4}{3/2} = \frac{4}{DR} \, \therefore \, DR = \frac{3}{2}$
$\therefore \, BD = BR - DR = 4 - \frac{3}{2} = \frac{5}{2}$
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Notes on Trigonometric Identities
Concepts Used:
Trigonometric Identities
Various trigonometric identities are as follows:
Even and Odd Functions
Cosecant and Secant are even functions, all the others are odd.
- sin (-A) = – sinA,
- cos (-A) = cos A,
- cosec (-A) = -cosec A,
- cot (-A) = -cot A,
- tan (-A) = – tan A,
- sec (-A) = sec A.
Pythagorean Identities
- sin2θ + cos2θ = 1
- 1 + tan2θ = sec2θ
- 1 + cot2θ = cosec2θ
Periodic Functions
- T-Ratios of (2π + x)
sin (2π + x) = sin x,
cos (2π + x) = cos x,
tan (2π + x) = tan x,
cosec (2π + x) = cosec x,
sec (2π + x) = sec x,
cot (2π+x)=cotx. - T-Ratios of (π -x)
sin (π–x) = sin x,
cos (π–x) = - cos x,
tan (π–x) = - tan x,
cosec (π–x) = cosec x,
sec (π–x) = - sec x,
cot (π–x) = - cot x. - T-Ratios of (π+ x)
sin (π+x) = - sin x,
cos (π+x) = - cos x,
tan (π+x) = tan x,
cosec (π+x) = - cosec x,
sec (π+x) = - sec x,
cot (π+x) = cot x. - T-Ratios of (2π – x)
sin (2π–x) = - sin x,
cos (2n–x) = cos x,
tan (2π–x) = - tan x,
cosec (2π–x) = - cosec x,
sec (2π–x) = sec x,
cot (2π-x) = - cot x
Sum and Difference Identities
- T-Ratios of (x + y)
sin (x+y) = sinx.cosy + cosx.sin y
cos (x+y) = cosx.cosy – sinx.siny - T-Ratios of (x – y)
sin (x–y) = sinx.cosy – cos.x.sin y
cos (x-y) = cosx.cosy + sinx.siny
Product of T-ratios
- 2sinx cosy = sin(x+y) + sin(x–y)
- 2cosx siny = sin(x+y) – sin(x–y)
- 2 cosx cosy = cos(x+y) + cos(x–y)
- 2sinx.siny = cos(x–y) – cos(x+y)
T-Ratios of (2x)
sin2x = 2sin x cos x
cos 2x = cos2x – sin2x
= 2cos2x – 1
= 1 – 2sin2x
T-Ratios of (3x)
sin 3x = 3sinx – 4sin3x
cos 3x = 4cos3x – 3cosx