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Maths >> Trigonometry >> General Trigonometry AIEEE

Prove that :-

sin(A+B+C+D) + sin(A+B-C-D) + sin(A+B-C+D) + sin(A+B+C-D) = 4sin(A+B).cosC.cosD

Asked By: ADARSH
is this question helpfull: 1 0 submit your answer
Joshi sir comment

sin(A+B+C+D) = sin(A+B)[cosCcosD-sinCsinD]+cos(A+B)[sinCcosD+cosCsinD]

similarly solve all the terms and add all these terms for getting answer

Maths >> Algebra >> Permutation and Combination IIT JEE

what will be the rank of word OPTION in the dictionary of words formed by letters of the word OPTION

Asked By: JIGYASA KUMAR
is this question helpfull: 13 6 submit your answer
Joshi sir comment

OPTION

ordered way INOOPT

total words = 6!/2! = 360

so rank = (360/6)*2+([60*2]/5)*3+(24/4)*3+(6/3)*0+(2/2)*1+1 = 120+72+18+0+1+1 = 212

 

Maths >> Calculus >> Functions IIT JEE

FIND DOMAIN OF f(x)=log4log3 log2x WHERE 4,3,2 ARE BASES ?

Asked By: SIDDHANT
is this question helpfull: 4 0 submit your answer
Joshi sir comment

f(x)= log4log3log2x 

so 0 < log3log2x < ∞

so 1 < log2x < ∞ 

so 2 < x < ∞

Maths >> Trigonometry >> General Trigonometry IIT JEE

((1(secA.secA-cosA.cosA))-(1/(cosecA.cosecA-sinA.sinA))).sinA.sinA.cosA.cosA=(1-cosA.cosA.sinA.sinA)/(2+cosA.cosA.sinA.sinA)

Asked By: VISHVESH CHATURVEDI
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Joshi sir comment

Submit the correct question, In first bracket / will be there so

((1/(secA.secA-cosA.cosA))-(1/(cosecA.cosecA-sinA.sinA))).sinA.sinA.cosA.cosA

= [cos2A/sin2A(1+cos2A) - sin2A/cos2A(1+sin2A)]sin2Acos2A

= [cos4A(1+sin2A) - sin4A(1+cos2A)] / [(1+sin2A)(1+cos2A)]

now solve

 

 

 

 

Maths >> Trigonometry >> General Trigonometry Olympiad

if x is any real number and cosA=x^2+1/2x then cos A value is 

 

Asked By: RAMACHANDRAM
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Joshi sir comment

x2+1 > 2x so cosA>1 which is not possible

Maths >> Trigonometry >> Trigonometrical Equations IIT JEE
2cos7x/cos(3)+sin(3)>2^cos2x
Asked By: AARSHI
is this question helpfull: 10 0 submit your answer
Joshi sir comment

Please submit what we have to do and also correct the question 

it is cos3 or cos3x 

Maths >> Trigonometry >> Trigonometrical Equations IIT JEE
(tanx)^2(tan3x)^2(tan4x)=(tanx)^2-(tan3x) ^2 + tan4x.
Asked By: AARSHI
is this question helpfull: 13 1 submit your answer
Joshi sir comment

I dont know what the question is but if the question is to solve this eq. then the method will be as given below

tan2x tan23x tan4x = tan2x  - tan23x + tan4x

so tan4x =  [tan2x  - tan23x] / [tan2x tan23x-1]

now split RHS terms by formula x2-y2= (x+y)(x-y)

so RHS = tan4xtan2x 

now solve

Maths >> Co ordinate Geometry >> General Coordinate Geometry IIT JEE

A(3,4) and B is a variable point on the line |X| = 6. Also, AB ≤ 4. Then the number of positions of B with integral co-ordinates is:

(a)5  (b) 6 (c) 10 (d) 12

 

Asked By: GAUTHAM GANESH
is this question helpfull: 8 2 submit your answer
Joshi sir comment

by diagram (6,4),(6,3),(6,2) are points having AB<4 besides it two upside points are also there by symmetry not shown in diagram. These points are (6,5) and (6,6)

Total no. of points = 5

Maths >> Statics >> Equilibrium under more than 3 forces IIT JEE

help me understand lamis theorem

 

 

 

 

Asked By: TANYE COLLINS KOFI
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Joshi sir comment

It is the theorem for the equilibrium of a body under 3 forces

According to the theorem if three forces are acting on a body and body is in equilibrium then 

P/sinA = Q/sinB = R/sinC

Maths >> Calculus >> Differential Equations Engineering Exam
Differential form of ol conics whose axes coincide with the co-ordinate axes??
Asked By: NEHA GUPTA
is this question helpfull: 19 3 submit your answer
Joshi sir comment

let us consider the case of ellipse with x and y axes as their axes

eq. is x2/a2 + y2/b2= 1

on differentiating we get 2x/a2 + 2yy'/b2 = 0                                y'is first differential

so yy'/x = -b2/a2

again differentiate and get answer. 

You should remember that you should differentiate as many times as the number of constants.

for ex. in the case of parabola only first diffrentiation is sufficient.

now complete it for all conics

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