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LHS = tan4x = tan(2x + 2x)

use, the formula, tan(A + B) = (tanA+tanB)/(1-tanA.tanB)

= (tan2x + tan2x)/(1-tan2x.tan2x)

=2tan2x/(1-tan²2x)

again, use the formula, tan2A = 2tanA/(1-tan²A)

= 2{2tanx/(1-tan²x)}/[1-{2tanx/(1-tan²x)}²]

=4tanx.(1-tan²x)²/(1-tan²x)(1+tan⁴x-2tan²x-4tan²x)

=4tanx.(1-tan²x)/(1-6tan²x+tan⁴x)

= RHS

The median for the coordinates of intersection point of less than ogive and more than ogive will be-The median of grouped data is the x-coordinate of the point of intersection of the two ogives. Here, the ‘less than ogive’ and ‘more than ogive’ intersect at (14.5, 20).so, median = 14.5

i) f(x) = x+1 , is always increasing in its domain and it has exactly one value for each of its domain so it is one-one

ii) f(x) = x³ , is also one - one

ii) f(x) = x+|x| is 0 for all x ≤0 , so it is not one-one

When roots are equal discrimanat must be 0.Here we have x² + 5kx + 16 = 0D = (5k)² - 4 × 16 = 0

(5k)² = 64

k² = 64/25

k = √(64/25)

k = + or - 8/5

k = 8/5 and -8/5

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how it became 5k square

Formula for discrimanat for equation ax² + bx + c = 0 is

D = b² - 4ac , that's the reason

oh now i understood thankyou soo much

Two digit numbers are : 10,11,12,....,,98,99

numbers divisible by 2 are 10, 12, 14, ...96,98. series APnumbers divisible by 5 are 15, 20,... , 90, 95 there are some common numbers in the two series: 20, 30, 40, ...,90.

A.P.Series1 = 10, 12, ..,96, 98 number of terms : (98-10)/2 + 1 = 45 S1 = (first term+last term)/2*number of terms = (10+98)/2*45 = 27*45=1215

sum of numbers divisible by 5 : number of terms = (95 - 15)/5 + 1 = 17 S2 = (95+15) / 2 * 17 = 55 * 17=935

Sum of numbers divisible by 10 : number of terms= (90-20)/10+ 1 = 8 S3 = (90+20)/2 * 8= 55 * 8=440

Answer = S1 + S2 - S3 =1215+935-440 =1710

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if x-a is a factor the x=a , is the zero of the polynomial x³-mx²-2nax+na²

so, (a)³-ma²-2na²+na² = 0=> a³-ma²-na² = 0 => a²(a-m-n) = 0so with a= 0, or a = m+n

thank you

ans.11ARITHMETIC PROGRESSIONa=14añ=98d=7añ=a+(n-1)d98=14+(n-1)7n=[(98-14)/7]-1n=13

2x + 3 = 9

2x = 9 - 3

2x = 6

x = 6/2 = 3

Therefore, value of x = 3

i) 5/7 is Greatestii) 2/3 = 0.666...4/5 = 0.85/6 = 0.8333so 5/6 is Greatest

24is the correct answer

24 is the correct answer.

two digit no are 10 to 99a= 12, d=4, an=96let n be the terma+(n-1)d=9612+(n-1)(4)=964n-4=96-12=844n= 84+4=88n= 88/4=22there are 22 term between 10 to 99 (two digit number) divisible by 4

n=22 is the best answer

formula an=a+(n-1)d 12,16,20.......96. n=? a=4 an=96 d=4 96=4+(n-1)4. 96=4+4n-4. 96=4n. n=96/4. n=24

24 is the correct answer

25 two digit no. are divide by 4

highest 2 digit no. = 98 a = 4 d =4 as A. P. = 4 ,8 ,12 ,16 .........96 as

an = a + (n-1)d96=4 + (n-1)496=4+4n-496=4nn=96÷4n=24

the last proof I guess is not correct u have to prove tanA/secA-1

Lowest two digit Number divisble 4 =12Highest two digit number divisible=96Putting formula An=a+(n-1)dAn is Highest number=96a is lowest=12D is 4so96=12+(n-1)496-12=4n-484+4=4n88=4nn=88/4n=22Total number=22

Smallest 8 digit number-10,000,000Greatest 7 digit number-99,99,999Difference-10,000,000-99,99,999=1

smallest number of 8 digit= 1,00,00,000greatest number of 7 digit= 99,99,999=1,00,00,000 - 99,99,999 =1

hey sorry but can you tell greatest six digit number long division method

Smallest 8 digit number-10,000,000Greatest 7 digit number-99,99,999Difference-10,000,000-99,99,999=1

79+x+40=180(linear pair)x=180-(79+40)x=180-(119)x=61°

use r=√h^2-l^2

formula and substitute

it's not coming

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The smallest three digit no is 100.

The largest three digit no is 999

If you divide the above two figures seperately by 18 you will get a quotient and a reminder. If the reminder is not zero you multiply the quotient incresed to the nearest whole number by 18 to get the smallest and largest three digit number divisible by 18. Add the two and divide the sum by 2 to get the average.

100÷18=5.5. 18*6=108

999÷18=55.55. 18*55=990

(108+990)=1098/2=549

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thank you

Let the unit digit be X and ten 's digit be Y. So, original digit be ( X+10.Y) , And by reversing the digit we get (Y+10.x)

SO ACCORDINGTO THE QUESTION

(X+10Y)+(Y+10X) = 66

11X+11Y = 66

11(X+Y) = 66

X+Y = 66/11

X+Y = 6 ------------------- 1

And, since digits differ by 2

So, X-Y = 2 --------------- 2

Adding 1 and 2 equations we get

2X = 8

X = 8/2

so, X = 4

And, puttingvalue of Xin equation 1

X + Y = 6

4 + Y = 6

Y = 6 - 4

Y = 2

Therefore, number is given by putting value of X & Y

Hence, number is ( 4+10*2) = 24...

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Lowest two digit Number divisble 4 =12HIghest two digit number divisble=96Putting formula An=a+(n-1)dAn is Highest number=96a is lowest=12D is 4so96=12+(n-1)496-12=4n-484+4=4n88=4nn=88/4n=22Total number=22

2 1/5 = 11/5

= 2.2

So, 2.2 is the multiplicative inverse of 2.2

333 1/3

= 333.33

333.33 is not the multiplicative inverse of 0.003

veryyyyy veryy thanks

12=2^2*316=2^418=2*3^2so LCM=2^4*3^2=144so number should be divisible by itso 9936 is the greatest number divisible by 144 so 9936 is exactly divisible by 12,16 & 18.

995 is the greatest 3 digit number divisible by 5

995 is divisible by 5

995 is divisible by 5 on the basis of 3 digit number

the greatest three digit number which is divisible by 5 is 995

the greatest three digit number which is divisible by 5 is 995

the greatest three digit number which is divisible by 5 is 995

The greatest three digit number which is divisible by 5 is 995

995 is the right answer of this question

995 is the right answer

The greatest three digit number which is divisible by 5 is 995

995 is the correct answer.

995 is the correct solution.

995 is the right answer.

995 is the best answer

995 is the right answer

The greatest three digits number is divisible by 5 is 995..Please like my answer..

hope it helps u

-3 1/7=-22/7hence the multiplicative inverse will be -7/22multiplicative inverse means that the product should be 1

Answer is 999999990.

999999990 is correct answer of following question

9999999990 is the correct answer

9999999990 is correct

999999990is your andwer

999999990 is right answer

999999990 is the right answer

Secθ+tanθ=p ----------------------(1)∵, sec²θ-tan²θ=1or, (secθ+tanθ)(secθ-tanθ)=1or, secθ-tanθ=1/p ----------------(2)Adding (1) and (2) we get,2secθ=p+1/por, secθ=(p²+1)/2p∴, cosθ=1/secθ=2p/(p²+1)∴, sinθ=√(1-cos²θ)=√[1-{2p/(p²+1)}²]=√[1-4p²/(p²+1)²]=√[{(p²+1)²-4p²}/(p²+1)²]=√[(p⁴+2p²+1-4p²)/(p²+1)²]=√(p⁴-2p²+1)/(p²+1)=√(p²-1)²/(p²+1)=(p²-1)/(p²+1)∴, cosecθ=1/sinθ=1/[(p²-1)/(p²+1)]=(p²+1)/(p²-1) Ans.

Total numbers between 4 and 102 98 numbersHence half of them are even hence divisible by 2Hence98/2=46