Question

HEYA.....Rhythm here :-)
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(1) WHICH OF THE
FOLLOWING IS NOT CORRECT ?

(A) Cos 1° > Cos 1

(B) Cos 1° < Cos 1

(C) Sin 1° = Cos 1

(D) Sin 1° = Sin 1
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(2) In A Triangle tanA + tanB + tanC = 6 and tanA tanB = 2 ,
then the values of tanA ,tanB and tanC are

(A) 1,2,3

(B) 2,1,3

(C) 1,2,0

(D) None of these
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■ Need full explaination with reason

◆ NO USELESS ANSWERS

● 30 POINTS

Answer 1

(1) 

cos 1 degree = 0.999

cos 1 radian = 0.540

sin 1 degree = 0.017

sin 1 radian = 0.841.

Option Verification:

(A) cos 1 degree > cos 1

= > True.


(B) cos 1 degree < cos 1

= > False


(C) sin 1 degree = cos 1

= > False

(D) sin 1 degree = sin 1

= > False.


Therefore the correct answer is - Option(A) : cos 1 degree > cos 1 radian.


(2) 

Given tanA + tanB+ tanC = 6 ------- (1)

Given tanAtanB = 2 

= > tanB = 2/tanA ----- (2)

Given A + B + C = 180

= > A + B = 180 - C

= > Tan(A + B) = Tan(180 - C)

= > TanA + TanB/1 - TanATanB = -Tanc

= > 6 - Tanc/1 - 2 = -Tanc

= > Tanc = 6 - Tanc

= > 2Tanc = 6

= > Tanc = 3

Substitute in (1), we get

= > tanA + tanB + 3 = 6

= > tanA + tanB = 3

= > tanA + 2/tanA = 3

= > tan^2A + 2 - 3tanA = 0

= > tan^2A - 2tanA - tanA + 2 = 0

= > (tanA - 1)(tanA - 2) = 0

= > tan A = 1 (or) 2 

Substitute A = 1 in (1), we get

= > 1 + tanA + 3 = 6

= > tanA + 4 = 6

= > tanA = 2


Substitute A = 2 in (2), we get

= > 2 + tanB + 3 = 6

= > tanB + 5 = 6

= > tanB = 1.



Therefore the value of tanA , tanB = 1 (or) 2  and tanC =3.



Hope this helps!